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\n
1. Introduction
\n
\n
1.1 Lophomonas blattarum\n
\n
It is an anaerobic multiflagellated intestinal protozoan, endocommensal in the intestine of some arthropods, such as termites and cockroaches (Dictyoptera: Blattoidea), which contaminate in its path food, dust and clothes with its secretions and feces [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11].
\n
The genus Lophomonas, since 1990, has been considered among the protozoa that cause damage to the respiratory tract, especially in immunocompromised individuals (HIV/AIDS, with neoplasms, and use of corticosteroids and transplants) and in adult and pediatric asthmatic individuals [2, 3, 4, 5, 6].
\n
The signs and symptoms of Lophomonas infection are similar to pneumonia and bronchitis or bronchopulmonary pathologies of various etiologies; therefore, a correct diagnosis is difficult. The above requires us to duly attend the microbiological study of expectoration, brushing, biopsy or bronchoalveolar lavage samples, whether fresh or stained preparations, especially when observing multiflagellated forms, since if you do not have enough experience trophozoites of Lophomonas blattarum can be confused with ciliated epithelial cell fragments (ciliocytoforia) of the bronchi [5, 6, 7].
\n
It is important to note that conventional techniques, such as staining of Gram, Giemsa and Papanicolaou smear, do not allow adequate visualization of multiflagellating. Therefore, it is necessary that upon suspicion, a fresh preparation with saline solution is first performed on all samples of the respiratory tract that arrive at the laboratory for parasitological diagnosis, and subsequently, perfectly extended smears are stained with special dyes such as Masson’s trichrome [5].
\n
The most clinically important species are Lophomonas blattarum and Lophomonas striata. The latter was the species first identified in the intestine of the cockroach Blatta orientalis by S. Stein in 1860 [6]. The structure of L. blattarum was identified in the optical microscope in 1911 and in 1990 with a scanning and electron microscope. The shape of the Lophomonas trophozoite is usually round, oval or pyriform, ranging in size from 15 to 50 μm in diameter, with a plume of flagella that form a bunch located at the anterior end, the largest being those found far away from the apical fissure. It contains phagocytic vacuoles in its cytoplasm, with outward rhythmic movements directed to the apical end in order to eliminate excretions or trap foreign materials [1] (Figure 1).
\n
Figure 1.
In the 1860s, S. Stein discovered some multiflagellates in the cockroach’s intestine. Drawings of the structures identified as Lophomonas blattarum and Lophomonas striata are shown [7].
\n
The cockroaches (Figure 2) originate as perfectly recognized pests of closed, dark places, which abound at the beginning of the hot climate and which become visible at night when leaving their natural habitat (sewers) to look for their food in the periphery and/or inside the houses [12]. As vectors were not considered capable of transmitting pathogenic organisms to humans, however, studies were conducted by Roth and Willis in 1957, and citing evidence occurred in a pediatric hospital in Brussels, Belgium, where an epidemic of Salmonella typhimurium persisted in newborns, despite the rapid isolation of patients, the absence of healthy carriers and the suppression of direct or indirect contact, except for the isolation of cockroaches. However, it was discovered that at night the cockroaches walked on the clothes, blankets and bodies of the babies, and the bacteria were isolated from the body of a considerable number of insects [13]. The epidemic ceased immediately after a severe control of the cockroaches. Rueger and Olson in 1969 showed that the feces of Periplaneta americana infected with Salmonella oranienburg, being spread over food and vessels, still contained live bacteria after 3.25–4.25 years [14]. These same authors provided a list of 18 species of domestic cockroaches; from which, it was possible to isolate the pathogenic organisms for man, due to its allergenic exposure or toxicity due to its bite [14] (Figure 2).
\n
Figure 2.
Home cockroach. Photo Villagrán-Herrera.
\n
Let us consider Cornwell’s paraphrase in 1968, which stated the following:
\n
(1) Cockroaches prefer environments where both human pathogens and human food are found, freely passing from one to the other; (2) cockroaches can carry pathogens both inside and outside their bodies, which remain viable on the cuticle in the digestive tract and feces to the extent that insects can be chronic carriers and (3) the evidence is sufficient to justify the various programs of control for this insects where human health is endangered [15].
\n
They are usually confined to buildings in cold climates, but domestic cockroaches can escape freely, and in temperate, tropical or hot weather, they can migrate to other buildings through drains, garbage dumps, septic tanks and latrines where they feed, both on human feces and on food. Isolates of intestinal diners from trapped cockroaches indicate that they are carriers of microorganisms (viruses, fungi and intestinal parasites). Among the viruses, there are 4 strains of poliovirus; and approximately 40 species of pathogenic bacteria (enterobacteria), the mycobacterium of leprosy, two pathogenic fungi (Aspergillus), and the protozoan Entamoeba histolytica are also mentioned. On the other hand, other pathogens that are harbored by these arthropods are mentioned under experimental conditions, such as Coxsackie virus, mouse encephalitis and yellow fever; the bacterial agents of cholera, cerebrospinal fever, pneumonia, diphtheria, undulant fever, anthrax, tetanus, tuberculosis and others; and the protozoa Pentatrichomonas hominis, Giardia intestinalis and Balantidium coli, agents that produce diarrhea or dysentery [13].
\n
A protozoan that is considered important is the sporozoan Toxoplasma gondii, which causes human toxoplasmosis and spreads in many mammals besides birds. This disease is common in humans, although asymptomatic, but it can cause congenital defects in the fetus. It has recently been shown that the biological cycle of this coccidium is limited to domestic cats and other felines [16]. Cats can become infected by feeding on parasitized birds and rodents and subsequently transmit the parasite in their feces and a cockroach that feeds on these debris can transmit the parasite to man. Chinchilla and Ruiz in 1976 demonstrated in Costa Rica the potential transmission of Toxoplasma gondii by domiciliary cockroaches to humans [17] (Figure 3).
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Figure 3.
Biological cycle of Toxoplasma gondii. You can see the cockroach enclosed in a red circle, like a transporter or possible reservoir of coccidium [16].
\n
These species of cockroaches in urban areas have been seen mainly in nurseries, schools or hospitals, where a certain number of their population had presented lung problems of various types, and these problems were not related to the presence of these insects. It was not until the year 2015 that Dalmiro Cazorla-Perfetti found in dissected intestines of some captured insects, in addition to eggs of geohelminths, trypanosomatids, cysts and trophozoites of a multiflagellated protozoan calledLophomonas blattarum [18] (Figure 4).
\n
Figure 4.
Cytoplasmic and multifoflous trophozoite forms of Lophomonas blattarum are observed 400× [19].
\n
On the other hand, in the city of Wuhan, in an intestinal study of 110 specimens of Periplaneta americana (pipe cockroach), they showed in preparations stained with Giemsa and seen at 1000 magnifications, oval, pearly shapes, from 20 to 40 μm, with a tuft of flagella extended down the central axis of the parasite and one of its trumpet-shaped ends enveloped the only nucleus shown. It also showed a thin terminal axostyle posterior to the multiflagellated part. Based on the above morphological characteristics, the parasite was identified as L. blattarum. Of the 110 cockroaches, 44 tested positive for Lophomonas blattarum (44%) [18] (Figure 5).
\n
Figure 5.
Structures found in the intestinal dissections of pipe cockroaches in the city of Wuhan. Staining [18].
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\n
\n
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2. Medical importance of arthropods
\n
The different ways in which arthropods are related to the health and well-being of man are classified into three groups:
Arthropods as direct agents of diseases or discomfort
Entomophobia. Including illusory parasitosis
Disturbances and blood loss
Accidental damage to sense organs
Poisoning
Dermatosis
Myiasis and associated infestations
Allergies and associated conditions
Arthropods as vectors or as intermediate hosts
Mechanical vectors (more or less casual transmission)
Mandatory vectors (including some degree of development within the arthropod)
Intermediary guests (as passive carriers)
Foretic carriers of harmful arthropods
Arthropods as natural enemies of medically harmful insects
Competitors
Predatory parasites
\n\n
The taxonomic scope of arthropods should be considered together with pentastomids, since the latter have always been considered as a phylum or class apart from the arthropods, however pentasthomids such as the Linguatula serrata whose adult forms live in the nose of dogs (and exceptionally in the human). Embryonated eggs are released via nasal mucosa or feces. If the intermediate hosts ingest the eggs, the primary four-legged larva emerges and migrates via blood vessels to the internal organs. When the final host ingests raw or undercooked meat from the infected intermediate host, the adult form develops in the nasal tract. These can be parasites of the respiratory tract and cavities of reptiles, birds and mammals. Humans can also be accidental hosts and can be infected by ingesting eggs that later develop nymphs in their tissues (visceral pentastomiasis), or ingest meat infected with nymphs in their tissues, developing in the nose and pharynx adult forms (nasopharyngeal pentastomiasis) or Halzoun disease [20].
\n
In 1973, Lavoipierre and Rajamanickam cited cockroaches as intermediate hosts of long-necked pentasthomids [21].
\n
\n
2.1 Nomenclature
\n
The modern system of naming and classifying animals dates from the 10th edition of Linnaeus Systema Naturae (1758), in which not only the first complete and ordered group of animals but also a new system of nomenclature appeared. It was Linnaeus who first devised the method of substituting specific unique names for the descriptive phrases that until then had been used in combination with the words that are now known as generic names. Linnaeus recognized six classes of animals; the fifth is the insect, whose definition allowed the inclusion of a large number of creatures that are no longer called insects, rather with their popular name, such as spiders, mites, crabs and centipedes. Its Insecta class was divided into seven orders; each of which contained several genera and each of which included numerous species [22].
\n
\n
\n
2.2 Order dictyoptera
\n
\n
2.2.1 Cockroaches and praying mantises
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The only members of this order that have any medical importance are the cockroaches (suborder Blattoidea) associated with man. These rather flattened insects, sometimes similar to beetles that move quickly, are familiar to most people; they can be easily distinguished from beetles by their very flexible, wire-like antennas [23].
\n
The cockroaches form an ancient group, which goes back to the Silurian and which has few changes in its general structure since the Devonian, around 320 million years ago. They were very abundant in the Carboniferous marshes, as indicated by their fossil remains in the coal deposits of that period. They are taxonomically admitted in a separate order together with the mantids, in the Dictyoptera or as a suborder of the Orthoptera, in addition to the evidences that show a strong ancestral relationship with the termites [24] (Table 1).
The species associated with man attack stored food and infest premises used for storing, preparing and cooking food, such as bakehouses and kitchens, as well as sewers and rubbish dumps. They are known to carry pathogenic viruses, bacteria and helminths and to act as intermediate host for such pathogens as the nematode Gongylonema pulchrum Molin (gullet worm) and the Acanthocephalus Moniliformis moniliformis Bremser; they are also capable of causing allergic dermatitis. More than a dozen species have some degree of medical importance, but the following six species, all with worldwide distributions, are the principal vectors: the common cockroach (Blackbeetle) (Blatta orientalis), the American cockroach (Periplaneta americana), the Australian cockroach (P. australasiae), the German cockroach (Blattella germanica), the brown-banded cockroach (Supella supellectilium* (Serville) and the Madeira cockroach (Leucophaea maderae).
\n
The following descriptions are key to identify the adults of six medically important species of cockroaches:
Well-developed forewings, reaching at least the tip of the abdomen.
Front wings absent or underdeveloped, not reaching the tip of the abdomen.
Total length (up to the tips of the front wing) more than 18 mm.
Total length (up to the tips of the front wing) less than 17 mm.
General grayish brown color, pronotum and front wings stamped (Figure 6F) \nLeucophaea maderae (Fab).
Front wings with a pale yellow stripe along the basal part of the anterior margin (Figure 6C) \nPeriplaneta australasiae (Fab).
Front wings without a pale yellow stripe along the basal part of the anterior margin (Figure 6B) American Periplaneta (L.).
Pronotum with two conspicuous longitudinal dark bands. Front wings uniform color (Figure 6D) Blattella germanica.
Pronotum without dark bands (brown with translucent lateral margins). Forewings dark basally and pale distally in the male, and dark with pale bands in the female (Figure 6E) Supella supellectilium(Serville).
Legs from reddish brown to dark brown. Uniformly opaque pronotum. Total length greater than 15 mm (Figure 6A) \nBlatta orientalis L.
\n\n
Figure 6.
Species of cockroaches of medical importance. A, C, D, E and F are vector agents of viruses, helminths and bacteria for both humans and animals. B is a host of the endocomponent Lophomonas blattarum, a multifilated protozoan [23].
\n
Young cockroaches are similar to those of adults but lack wings [25] (Figure 6E and F).
\n
The legs of insects are mainly for walking or running. The prominent antennas are filiform and multiarticulate. The mouthparts are of the generalized biting-chewing type (Orthoptera type). In most species, there are two pairs of wings; in some, the wings are vestigial, and in others, for example in Blatta orientalis, they are well developed in the male and short in the female. The outer pair of wings (tegmina) is narrow, thick and coriaceous; the inner pair is membranous and folds like a fan. It is assumed that the common name in English, cockroach, is derived from the pronunciation of Cockroach name in Spanish (koo-kah-rah-chah) [24].
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\n
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3. Presentation of a clinical case
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This is a 60-year-old male doctor by profession, originally from Pachuca Hidalgo, who has lived in the municipality of Cadereyta for 18 years. Denies trips abroad, without physical activity, and indicates adequate personal hygiene. He refers to the diagnosis 9 years ago of non-Hodgkin lymphoma and is in treatment with radiotherapy and chemotherapy. Due to edema after treatment, thoracocentesis and pericardiocentesis were performed, as well as gastrostomy, which he maintained for 1 year. Six months ago, he presented with respiratory symptoms, characterized by fever, malaise, cough with expectoration, and data of mild respiratory insufficiency. It is treated with antibiotics, and salbutamol is administered; however, the symptoms reappear after 15 days.
\n
One month ago, he presented with respiratory symptoms with the same characteristics, and he reported that a chest X-ray was performed with unspecified pneumonia data. Presents 6 days ago asthenia, adynamia, hyporexia, malaise, fever of 38.5°C, self-medicated Levofloxacin 750 mg every 12 h, Ceftriaxone 1 g every 24 h, Paracetamol and Metamizol 500 mg orally. Three days later, productive cough is added, expectoration with blood streaks, and later, it becomes a uniform reddish color; likewise, the cough persists and the amount of phlegm increases. There is mild dyspnea and no predominance of hours, and salbutamol is self-medicated, showing improvement with the application of the medication. Currently fever, general malaise and mild headache persist. Freshly emitted specimens of sputum are requested and fresh observations are made with saline and several smears, which are stained with Hematoxylin and Eosin (H/E), Papanicolaou and Giemsa. The study on fresh smears reveals trophozoites and cysts of a protozoan multiflagellate identified as Lophomonas blattarum (Figure 7a and b).
\n
Figure 7.
(a and b) Wet assembly with saline solution, where trophozoites and cysts of Lophomonas blattarum are observed. 400×. Photo Villagrán-Herrera.
\n
A large amount of polymorphonuclear leukocytes was observed in the smears before staining, coinciding with an acute inflammatory process (Figure 8).
\n
Figure 8.
Wet assembly with saline solution. Multiflagellated trophozoites and cysts were observed in a sample of unstained morning sputum. The vacuole and the many flagella in its narrow part are seen in some forms. These characteristics are compatible with Lophomonas blattarum. Erythrocytes are seen that reveal a throat bleeding process. 400×. Photo. Villagrán-Herrera.
\n
After the identification of the multiflagellated protozoan, treatment with metronidazole of 500 mg every 8 h was started orally for 7 days, improving symptoms, decreasing dyspnea and continuing with unproductive cough. Control studies are carried out 15 days after the last antiparasitic intake, and the samples were negative for the presence of this protozoan.
\n
\n
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4. Discussion
\n
To the cases reported in Peru, China and Spain (Table 2), where they found this protozoon in sputum samples, we must add 1 case recorded of a sinusitis in Iran [9], and this one that we are presenting from Mexico, since they have in common denominator deficiencies in the immune system, which makes them extremely sensitive to any infection no matter how mild. It also indicates a possible airborne transmission, with the influence of a humid environment through waste and environmental dust, and that by aspiration, the trophozoites or protozoan cysts can lodge in the bronchopulmonary epithelium, developing the infection with manifestations similar to any bacterial or fungal pulmonary pathology, which makes diagnosis even more difficult.
Reported cases of bronchopulmonary diseases with Lophomonas blattarum [5, 6, 7, 8, 9, 10].
Two more cases have been added. From Peru and Mexico. It is presumed that in the world, there may be many more cases that have not been reported.
\n
Our patient presented with respiratory symptoms that indicated possible miliary tuberculosis or some acute respiratory pathology, since in the expectorant product blood threads were observed in some of the emissions, so that without the saline solution wet study, the differential diagnosis would not have been possible to reach.
\n
The immunological commitment of the patient was a crucial and decisive factor for the development of the infection, as self-medication and the lack of an accurate diagnosis were important factors to delay his full recovery.
\n
\n
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5. Conclusions
\n
This particular case has been the first diagnosed in the city of Querétaro and reported in the Mexican Republic and illustrates casual infection of L. blattarum, a rare opportunistic pathogen, probably acquired by air, developing the patient’s lung infection, due to his immunocompromised state. It is essential that doctors consider Lophomonas blattarum in their differential clinical diagnosis. Since some dust mites are vectors of similar flagellates, whose respiratory manifestations are due to allergy, are similarly presented and are due to lack of an accurate diagnosis, they are transformed into chronic allergies without response to the administered treatment. Regarding the staining procedures applied to the biological sample of our patient, a great difference was observed between the multifilated structures worked in fresh and with saline solution, finding more clearly in the fresh and staining of Hematoxylin and Eosin, than with preparations with Pap smears and Giemsa (Figure 9).
\n
Figure 9.
Expectoration samples stained with Papanicolaou, Hematoxylin and Eosin (H/E) and with Giemsa, respectively. Observed at 400 X. with immersion oil. Note the difference in the observation of the parasites with each of the staining procedures. Photo Villagrán-Herrera.
\n
\n
Acknowledgments
\n
The collaboration and support of H.T. Evelyn Flores Hernández, the Department of Pathology of the Faculty of Medicine of UAQ, are acknowledged.
\n
Conflict of interests
The authors declare that there is no conflict of interest in relation to the publication of this clinical case.
\n',keywords:"American periplaneta, multiflagellated protozoan, bronchopulmonary lophomoniasis, endocommensal, immunosuppression",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/69242.pdf",chapterXML:"https://mts.intechopen.com/source/xml/69242.xml",downloadPdfUrl:"/chapter/pdf-download/69242",previewPdfUrl:"/chapter/pdf-preview/69242",totalDownloads:722,totalViews:0,totalCrossrefCites:0,totalDimensionsCites:0,totalAltmetricsMentions:0,impactScore:0,impactScorePercentile:43,impactScoreQuartile:2,hasAltmetrics:0,dateSubmitted:"May 16th 2019",dateReviewed:"August 17th 2019",datePrePublished:"September 25th 2019",datePublished:"June 17th 2020",dateFinished:"September 25th 2019",readingETA:"0",abstract:"Infection in humans by the intestinal protozoan of cockroaches and termites called Lophomonas blattarum has been diagnosed in respiratory infections of children aged 2–5 years contaminated orally or by air, with cysts or trophozoites contained in the feces of the cockroach Periplaneta americana. In respiratory infections of adults, it is difficult to diagnose since the cyst or trophozoite is not recognized as a human pathogen and is only related to immunosuppressed patients, transplant patients with severe lung disease and those living in poor and unhealthy sanitary conditions. Normally, its presence is manifested with fevers of 38–39°C, cough with thick expectoration, respiratory insufficiency and pulmonary abscesses. The laboratory diagnosis is mainly based on bronchoscopic cytologies and bronchoalveolar lavage biopsies. The case in question is about a 60-year-old male. Single, he lives alone, with a diagnosis of 9 baths behind non-Hodgkin lymphoma, undergoing treatment with radiotherapy and chemotherapy. For edema after treatment, thoracentesis and pericardiocentesis were performed, as well as gastrostomy, which he maintained for 1 year. He started with throat discomfort, followed by production of productive cough without blood, general weakness, and difficulty breathing, with apparent diagnosis of possible respiratory failure due to mycobacteria. It was possible to visualize the protozoan, in fresh preparations of bronchial aspirate and expectoration in wet assembly with saline solution and stained with Pap smears, Harris Hematoxylin and Eosin (H/E), and Giemsa.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/69242",risUrl:"/chapter/ris/69242",book:{id:"9025",slug:"parasitology-and-microbiology-research"},signatures:"Maria Elena Villagrán-Herrera, Ricardo Francisco Mercado-Curiel, José Trinidad López-Vázquez, Maria del Carmen Aburto-Fernández, Nicolás Camacho-Calderón, Javier Ávila-Morales and José Antonio De Diego-Cabrera",authors:[{id:"210676",title:"Dr.",name:"Maria Elena",middleName:null,surname:"Villagrán Herrera",fullName:"Maria Elena Villagrán Herrera",slug:"maria-elena-villagran-herrera",email:"mevh@uaq.mx",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:{name:"Autonomous University of Queretaro",institutionURL:null,country:{name:"Mexico"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_1_2",title:"1.1 Lophomonas blattarum\n",level:"2"},{id:"sec_3",title:"2. Medical importance of arthropods",level:"1"},{id:"sec_3_2",title:"2.1 Nomenclature",level:"2"},{id:"sec_4_2",title:"2.2 Order dictyoptera",level:"2"},{id:"sec_4_3",title:"Table 1.",level:"3"},{id:"sec_7",title:"3. Presentation of a clinical case",level:"1"},{id:"sec_8",title:"4. Discussion",level:"1"},{id:"sec_9",title:"5. Conclusions",level:"1"},{id:"sec_10",title:"Acknowledgments",level:"1"},{id:"sec_13",title:"Conflict of interests",level:"1"}],chapterReferences:[{id:"B1",body:'\nGile G, Slamovits C. Phylogenetic position of Lophomonas striata Bütschli (Parabasalia) from the hindgut of the cockroach Periplaneta americana. Protist. 2012;163(2):274-283\n'},{id:"B2",body:'\nZerpa R, Ore E, Patiño L, Espinoza Y. Hallazgo de Lophomonas sp. en secreciones del tracto respiratorio de niños hospitalizados con enfermedad pulmonar grave. 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A study on the differential diagnosis of ciliated epithelial cells from Lophomonas blattarum in bronchoalveolar lavage fluid. Zhonghua Jie He He Hu Xi Za Zhi. 2013;36(9):646-650\n'},{id:"B8",body:'\nStein S. Vortrag über die bisher unbekannt gebliebene Leucophyrs patula Ehbg.und über zwei neue infusoriengattungen Gyrocorys und Lophomonas. Abh Böhmisch Ges Wiss. 1860;1:44-50\n'},{id:"B9",body:'\nBerenji F, Parian M, Fata A, Bakhshaee M, Fattahi F. First case report of sinusitis with Lophomonas blattarum from Irán. Case Reports in Infectious Diseases. 2016;16:Article ID 2614187. DOI: 10.1155/2016/2614187\n'},{id:"B10",body:'\nMartínez-Girón R, van Woerden C. Lophomonas blattarum and bronchopulmonary disease. Journal of Medical Microbiology. 2013;62(11):1641-1648. DOI: 10.1099/jmm.0.059311-0\n'},{id:"B11",body:'\nLi R, Gao Z-C. Lophomonas blattarum infection or just the movement of ciliated epithelial cells? 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Cockroaches as possible transport host of Toxoplasma gondii in Costa Rica. Journal of Parasitology. 1976;62:140-142\n'},{id:"B18",body:'\nYang JX, Tang YY, Fang ZM, Tong ZZ, Li YL, Wang T. Investigation on Lophomonas blattarum infection in Periplaneta americana in Wuhan City. Zhongguo Ji Sheng Chong Xue Yu. 2014;32(2):161-162 (in Chinese)\n'},{id:"B19",body:'\nCazorla-Perfetti D, Moreno PM, Yamarte PN. Identification of Lophomonas blattarum (Hypermastigia: Cristomonadida, Lophomonadidae), causal agent of bronchopulmonary lophomoniasis in synanthropic cockroaches from the Coro university hospital, falcon state, Venezuela. Saber. 2015;27(3):511-514\n'},{id:"B20",body:'\nSchmidt GD, Roberts LS. Foundations of Parasitology. San Luis: CV. Mosby; 1977. 604 pp\n'},{id:"B21",body:'\nLavoipierre MMJ, Rajamanickam. Experimental studies on the life cycle of a lizard pentastomid. Journal of Medical Entomology. 1973;10:301-302\n'},{id:"B22",body:'\nLinnaeus 10ª. Edición del Sistema Nature, 1758. 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Internal Medicine Journal. 2011;50(9):1039-1043\n'},{id:"B29",body:'\nKang JF, Wu ML, Zhang W, et al. Parasitic Lophomonas in the people cysts of lung, a case report clinical focus. 2008;1:63-65\n'},{id:"B30",body:'\nLiu J et al. Diagnosis and treatment of Lophomonas blattarum infection in 26 patients with bacterial pneumonia. Journal of Thoracic Imaging. 2009;24(1):49-51\n'},{id:"B31",body:'\nLiu P, Oi LY, Lei DL, Chen SM. A case of pulmonary Lophomonas blattarum infection. Chinese Journal of Integrative Medicine. 2007;665:8 (in Chinese)\n'},{id:"B32",body:'\nMartínez-Girón R, Ribas A, Astudillo-González A. Flagellated protozoa in cockroaches and sputum: The unhygienic connection? Allergy Asthma. 2007;28:608-609\n'},{id:"B33",body:'\nMartínez-Girón R, Doganci L. Lophomonas blattarum: A bronchopulmonary pathogen. Acta Cytologica. 2010;54(Suppl):1050-1051\n'},{id:"B34",body:'\nMiao M, Wu DP, Sun AN, Yan LZ. Pulmonary Lophomonas blattarum infection in a patient with allogenic hematopoietic stem cell transplantation. Chinese Journal of Integrative Medicine. 2008, 2010;47:837-838 (in Chinese)\n'},{id:"B35",body:'\nShi YL, Li LH, Liao Y, Li XN, Huang XY, Liu J, et al. Diagnosis and treatment of Lophomonas blattarum infection in 26 patients with bacterial pneumonia. Zhonqquo Ji Sheng Chong Xue Yu Ji Sheng Chong Bing Za Zhi. 2007;25:430-431 (article in Chinese)\n'},{id:"B36",body:'\nWang K. A case of Lophomonas blattarum infection in lung. Zhongguo Ji Sheng Chong Xue Yu Ji Sheng Chong Bing Za Zhi. 2012;30:1 (in Chinese)\n'},{id:"B37",body:'\nWang Y, Tang Z, Ji S, Zhang Z, Chen J, Cheng Z, et al. Pulmonary Lophomonas blattarum infection in patients with kidney allograft transplantation. Transplant International. 2006;19(1006):1013\n'},{id:"B38",body:'\nYang YP, Dong HF, Wang RF. One case of Lophomonas blattarum in sputum. 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The treatment of bronchopulmonary Lophomonas blattarum infection: One case report and literature review. Journal of Clinical Pulmonary Medicine. 2008;12:15 (in Chinese)\n'},{id:"B44",body:'\nYao GZ, Cheng SK, Chang ZS. One case of bronchopulmonary infection with Lophomonas blattarum. Zhonghua Jie He He Hu Xi Za Zhi. 1999;22:507 (in Chinese)\n'},{id:"B45",body:'\nZhang F, Li YS, Zhang HX, Cai LM, Wu ZX. Clinical treatment on two cases with bronchopulmonary Lophomonas blattarum infection. Journal of Clinical Medicine Practice. 2010;14:83-84 (in Chinese)\n'},{id:"B46",body:'\nZhang RS, Lu L, Zhang DH, Wang X, Liu YX. Pulmonary Lophomonas blattarum infection in a patient with liver allograft transplantation. Chinese Journal of Organ Transplantation. 2010;31:767-768 (in Chinese)\n'},{id:"B47",body:'\nZhang X, Xu L, Wang LL, Liu S, Li J, Wang X. Bronchopulmonary infection with Lophomonas blattarum: A case report and literature review. The Journal of International Medical Research. 2011;39:944-949\n'},{id:"B48",body:'\nZhou Y, Zhu J, Li M. Report on two cases of bronchopulmonary infection with hypermastigote and review of the literature. Zhonghua Jie He He Hu Xi Za Zhi. 2006;29:23-25 (in Chinese)\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Maria Elena Villagrán-Herrera",address:"mevh@uaq.mx",affiliation:'
Department of Biomedical Research, Faculty of Medicine, Autonomous University of Queretaro, Mexico
'},{corresp:null,contributorFullName:"Ricardo Francisco Mercado-Curiel",address:null,affiliation:'
Department of Biomedical Research, Faculty of Medicine, Autonomous University of Queretaro, Mexico
Department of Biomedical Research, Faculty of Medicine, Autonomous University of Queretaro, Mexico
'},{corresp:null,contributorFullName:"José Antonio De Diego-Cabrera",address:null,affiliation:'
Department of Preventive Medicine, Public Health and Microbiology, School of Medicine, Autonomous University of Madrid, Spain
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1. Introduction
Probably the foremost unsolved problem in Graph Theory is Ulam’s Conjecture. This problem is due to P.J. Kelly and S.M. Ulam. Kelly’s Ph.D thesis [1] written under S.M.Ulam in 1942 dealt with this. Ulam proposed it as a set theory problem in his famous book “A Collection of Mathematical Problems” [2].
This is how Ulam’s problem was originally stated [2]:
Suppose that E and F are two sets, each containing m elements such that there is defined a distance function μ for every pair of distinct points, with values either 1 or 2, and μpp=0. If, for every subset of n−1 points of E, there exists an isometric system of m−1 points of F and the number of distinct subsets isometric to any given subset of m−1 points is the same in E and in F, then does E and F isometric?
There are many restatements of Ulam’s original conjecture, each dealing with another way of talking about sets. Kelly [3] has given the graph theoretic version of this problem as below and solved it for trees and disconnected graphs, and verified it for graphs on up to six vertices.
Theorem 1.1.(Ulam Conjecture).
Let G and H be graphs with VG=v1,v2,⋯,vn and for n≥3. If G−vi≅H−ui, for all then G≅H.
Many graph theorists have found other ways to restate the Ulam Conjecture. But the current version of this problem, popularly known as the Reconstruction Conjecture is the one formulated by Frank Harary [4].
Theorem 1.2. (Reconstruction Conjecture).
Every graph on at least three vertices is uniquely determined up to isomorphism by the collection of its one vertex-deleted subgraphs.
Graphs obeying the above conjecture are said to be reconstructible. Many classes of graphs and some parameters of graphs are already proved to be reconstructible. The papers [5, 6] and the book [7] deal with earlier work done on this problem. P. J. Kelly first proved that trees are reconstructible; but the proof is quite lengthy. A short proof was given by Greenwell and Hemminger using a powerful but simple counting theorem. This chapter deals with the counting theorem and its subsequent applications; also it ends up with a reduction of the Reconstruction Conjecture using distance and connectedness, which may lead to the final solution of the conjecture.
2. Reconstructible parameters and graphs
A vertex-deleted subgraph of a graph G, is called a card of G. The collection of all cards of G is called the deck of G and is denoted by DG.
Note that the graphs in the deck are unlabelled and, if G contains isomorphic vertex-deleted subgraphs, then such subgraphs are repeated in DG according to the number of isomorphic subgraphs that G contains. Therefore DG is a multiset, rather than a set, of isomorphism type of graphs.
Figure 1 shows an example of a graph and its deck.
Figure 1.
Graph and its deck.
A graph H with deck DH=DG is called a reconstruction of G. If every reconstruction of G is isomorphic to G, then G is said to be reconstructible. A graph that is not reconstructible is given by G≅K2 because, if H is the graph consisting of two isolated vertices, then clearly H is a reconstruction of G but it is not isomorphic to G. A property p defined on a class F of graphs is called a recognizable property if pG=pH whenever G∈F and H is a reconstruction of G. A classC of graphs is said to be recognizable if for all graphs G in C, any reconstruction of G must be in C. A parameterθ=θG is said to be reconstructible if for all reconstructions H of G, θH=θG. In other words θG is reconstructible if it can be determined uniquely from the deck of G. A classC of graphs is said to be reconstructible if every graph in C is reconstructible. A class C of graphs is said to be weakly reconstructible if for all graphs G in C, any graph in C that is a reconstruction of G is isomorphic to G.
Theorem 1.3. If G is a pq-graph with p≥3, then p and q are reconstructible.
Proof. It is trivial to determine the number p, which is necessarily one greater than the order of any subgraph G−v. Also, p is equal to the number of subgraphs G−v. To determine q, label these subgraphs by Gi,i=1,2,…p, and suppose Gi≅G−vi, where vi∈VG. Let qi denote the size of Gi. Consider an arbitrary edge e of G, say e=vjvk. Then e belongs to p−2 of the subgraphs Gi, namely all except Gj and Gk.
Hence,
∑i=1pqi
counts each edge p−2 times. That is,
∑i=1pqi=p−2q
Therefore,
q=∑i=1pqip−2
Corollary 1.4. Given a graph G−v in the deck of G=pq, the degree of v and the degrees of the neighbors of v in G are reconstructible.
Proof. The degree of v in G is simply q−EG−v, and this is reconstructible since q is. Therefore d, the degree sequence in nondecreasing order of G, is reconstructible.
Let d′ be the degree sequence of G−v but with the degree of v inserted in its correct position. The nonzero entries of the vector difference d−d′ occur in positions corresponding to neighbors of v in G, and their degrees can be read off from d.
Example 1.5. We illustrate Theorem 1.3 and Corollary 1.4 with the six subgraphs G−v shown in Figure 2 of some unspecified graph G. From these subgraphs we determine p,q, and degvi for i=1,2,...6. Clearly p=6. By calculating the qi,i=1,2,...6, we find that q=9. Thus, degv1=degv2=2,degv3=degv4=3, and degv5=degv6=4.
Figure 2.
Deck of the graph G.
Theorem 1.6.The connectivityκGof a graphGis reconstructible.
Proof. A graph G is disconnected if and only if κG=0. If G is connected and let κG = k≥1. Then there exists a set of k-vertices, say v1,v2,…,vk in VG such that G−v1v2…vk is disconnected and the removal of any set of fewer than k-vertices from G do not separable G. It follows that κG−vi=k−1 for i=1,2,…,k and κG−v≥k−1 for v∈VG=v1v2…vk. Hence for a connected graph G, κG−minv∈VGκG−v+1. Since the R.H.S. of the above equation is known from the deck of G, κG is reconstructible.
Theorem 1.7.If a graphGis reconstructible, then the complementG¯ofGis reconstructible.
Proof. Let G¯−v1G¯−v2…G¯−vn be the given deck of G¯. Then G¯−v1¯G¯−v1¯…G¯−vn¯=G−v1G−v2…G−vn. Therefore, DG is known. Since G is reconstructible, G can be obtained uniquely (up to isomorphism) from DG Hence G and so G¯ is known. That is, G¯ is reconstructible.
Theorem 1.8. Regular graphs are reconstructible.
Proof. From the deck of G, the degree sequence is reconstructible. Therefore, from DG it can be determined whether G is regular and if it is, its degree r is reconstructible.
Thus without loss of generality, we may assume that G is an r−regular graph with VG=v1,v2,…,vp,p≥3. Take any G−vi in the deck. The only way to reconstruct a regular graph of degree r from G−vi is to add a new vertex vi joining it to all the vertices of degree d−1 in G−v. Hence G is uniquely reconstructible.
Theorem 1.9. For graphs of order at least 3, connectedness is a recognizable property. In particular, if G is a graph with VG=v1,v2,…,vp,p≥3, then G is connected if and only if at least two of the subgraphs G−vi are connected.
Proof. Let G be a connected graph. By theorem G contains at least two vertices that are not cut-vertices. Let v1 and v2 be two vertices that are not cut-vertices. Then, clearly G−v1 and G−v2 are connected.
Conversely, assume that there exists vertices v1,v2∈VG such that both G−v1 and G−v2 are connected. Thus, in G−v1 and also in G, vertex v2 is connected to vi,i≥3. Moreover, v1 is connected to each vi,i≥3 in G−v2 and thus in G. Hence every pair of vertices of G are connected and so G is connected.
Remark 1.10. Since connectedness is a recognizable property, it is possible to determine from the subgraphs G−v,v∈VG, whether a graph G of order at least 3 is disconnected.
Theorem 1.11. Disconnected graphs of order at least 3 are reconstructible.
Proof. We have already noted that disconnectedness in graphs of order at least 3 is a recognizable property. Thus, we assume without loss of generality that G is a disconnected graph with VG=v1,v2,…vp,p≥3. Further, let Gi=G−vi for i=1,2,…p. Hence, if G contains an isolated vertex, then G is reconstructible. Assume that G has no isolated vertices. Among all the components of all the graphs in DG, let C be one with maximal number of vertices. Then C must be a component of G. Let v0 be a vertex of C that is not a cut vertex. Consider all graphs in DG that have the least number of components isomorphic to C. Among these, let G−v be the one with the largest number of components isomorphic to C=v0. Then the only way to form G from G−v is by replacing one component C−v0 by C.
Theorem 1.12. Separable graphs G without end vertices are reconstructible.
Proof. If the given deck of G contains two connectred cards and one disconnected cards, then G must be connected and containing a cut vertex and so it separable. Therefore, since the degree sequence of a graph is reconstructible, the class of all separable graphs without end vertices is recognizable. Throughout this proof, blocks mean rooted blocks where roots are the cut vertices of the graph that are in the blocks. The largest end blocks of G are identified as the the largest end blocks in all cards G−v. Let B be the one of the largest end blocks of G and the unique cut vertex in B is indicated in that card G−v. If any non-cut vertex w of B is deleted from B, then new rooted blocks are produced. Suppose that among the blocks so produced B1 is the largest, B2 the next largest (or another largest) and so on. Among all such vertex-deletions B−w, some of them must produce a maximum number, say k1 of B1‘s. Among all those vertex-deletions B−w producing k1 of B1‘s, some of them must produce a maximum number, say k2 of B2‘s, and so forth.
Now consider a card G−u showing a minimum number of blocks B, and a maximum number of blocks B1, B2, and so forth (in that order), all with roots as marked. Then the card G−u will show all blocks of G, except for one B, plus k1B1‘s, k2B2‘s, and so forth. Thus we can find all end blocks of G, with cut vertices marked. Let D be some smallest end block of G. Now choose a connected card G−v in which there is a smaller number of end blocks D than in G. Then G−v must have resulted from deletion of a vertex from D. Since G has no end vertices, the leftovers D−v is a nontrivial subgraph of G. That leftovers can be identified by considering first the smallest connected subgraph, say D′ of G−v containing all end blocks smaller than D. If D′ has ∣D∣−1 vertices, it is the leftovers of D. Otherwise, add to D′ the (unique) block which joins it to the rest of G. Continue adding blocks in that way until the resulting subgraph B contains ∣D∣−1 vertices. Then G can be recovered by replacing B by D, using the same cut vertex of attachment. Hence G is reconstructible.
Definition 1.13. For graphs F and G we denote by sFG the number of non-identical subgraphs F0 of G such that VF0⊆VG,EF0⊆EG and F0≅F.
In his thesis [1], Paul J. Kelly proved that for any two graphs F and G with VF<VG, the number of subgraphs of G isomorphic to F is reconstructible from the deck of G. Greenwell extended this result as follows: Let P denote a graphical property. If F is a subgraph of G having property P, then the number of subgraphs of G that are isomorphic to F and maximal with respect to property P is reconstructible from the deck of G.
Theorem 1.14. (Kelly’s Lemma) Let F and G be graphs of orders p1 and p respectively, where p1<p. Then the number sFG is recognizable from the subgraphs G−v,v∈VG.
Proof. Each subgraph of G isomorphic to F occurs in exactly p−p1 subgraphs G−v,v∈VG. Therefore,
p−p1sFG=∑v∈VGsFG−v
Since the numerator of the right hand side of this equation is recognizable and p and p1 are known, sFG is recognizable. Also,
sFG=∑v∈VGp−p1
3. Counting theorem
Let P denote a graphical property (such as being connected, being n-connected for some n≥2 or being planar, for example).Let G be a given graph, and let F be a graph such that F has property P and F⊂G, that is, sFG≥1. By an FG−chain with respect toP,we mean a sequence of pairwise nonisomorphic subgraphs of G such that each subgraph has property P and
F≅F0⊂F1⊂F2⊂⋯⊂Fn⊂G
where VF0⊆VF1⊆⋯⊆VFn⊆VG and EF0⊆EF1⊆⋯⊆EFn⊆EG.
The chain F0F1F2⋯Fn is said to have length n. Two FG−chains with respect to a property P are called isomorphic if they have the same length and corresponding terms are isomorphic graphs. The rank of F in G (with respect to P) is the maximum length among all FG−chains with respect to P.
Let F be a subgraph of a graph G such that F has a graphical property P. Then F is said to be a maximal subgraph with respect toP if VF⊆VG and EF⊆EG, and if, whenever H is a subgraph of G having property P such that VF⊆VH⊆VG and EF⊆EH⊆EG, it follows that F=H. For example, if P1 is the property of being connected, then a subgraph F of a graph G is a maximal subgraph with respect to P1 if and only if F is a component of G. If P2 denotes the property of being a block, then F is a maximal subgraph with respect to P2 if and only if F is a block of G.
Let P denote a graphical property and let G be a given graph. If F is a subgraph of G having property P, then by 54mPFG we mean the number of subgraphs of G that are isomorphic to F and maximal with respect to property P. For example, if P2 denotes the property of being a block and F≅K3, then for the graph G of Figure 3, it follows that sFG=6 and mPFG=2.
Figure 3.
The number of subgraphs with a specific property.
Theorem 1.15.(Counting Theorem). Let G be a graph of order at least 3, and let P be a graphical property. Suppose that each subgraph of G with property P has order less than of G. If for each subgraph F of G with property P and for each graph F0≅F such that VF0⊆VG and EF0⊆EG, there is a unique subgraph H of G that is maximal with respect to P such that VF0⊆VH and EF0⊆EH, then for each subgraph F of G having property P, the number mPFG is recognizable.
Proof. Let F be a subgraph of G such that F has property P.
By hypothesis, the order of F is less than the order of G. Denote the rank of F in G by r.
We show that
mPFG=∑n=0r∑−1nsFF1sF1F2⋯sFn−1FnsFnGE1
where the inner sum is taken over all pairwise nonisomorphic FG−chains F0F1⋯Fn of length n. (Note that all FG−chains can be determined since each is contained in some G−v, v∈VG.)
We verify (Eq. (1)) by induction on r. If r=0, the only FG−chain is the trivial F0, where F0≅F. This implies that each subgraph of G that is isomorphic to F is, in fact, a subgraph that is maximal with respect to P. Thus mPFG=sFG and (Eq. (1)) holds in the case where r=0. Let r be a positive integer, and assume that (Eq. (1)) is true for all subgraphs F of G with property P and having rank less than r. Let F be a subgraph of G having property P and rank r in G. By hypothesis, for each graph F0≅F such that VF0⊆VG and EF0⊆EG, there is a unique subgraph H of G that is maximal with respect to P such that VF0⊆VH and EF0⊆EH. Thus, the number of subgraphs of G isomorphic to F that are subgraphs of maximal subgraphs isomorphic to H is given by sFH.mPHG. Hence, if we sum these numbers over all nonisomorphic subgraphs H of G having property P, then we obtain the total number of subgraphs of G isomorphic to F. In symbols,
sFG=∑sFH.mPHG
where the sum is taken over all nonisomorphic subgraphs H of G having property P. Since sFH=1 if H≅F, we have
mPFG=sFG−∑H≠FsFH.mPHGE2
In (Eq. (2)) it suffices to consider only those subgraphs H of G having property P for which sFH>0. Since any such subgraph H has rank less than r, the inductive hypothesis can be applied to each term mPHG, yielding
mPFG=sFG−∑sFG∑m=0rankH∑−1msHH1sH1H2⋯sHmGE3
where the inner sum is taken over all pairwise nonisomorphic HG-chains H0H1⋯Hm of H of G having property P such that sFH>0 and H≠F. Redistributing the summations in (Eq. (3)), we obtain
mPFG=sFG−∑∑m=0rankH∑−1msFHsHH1⋯sHmG
or equivalently,
mPFG=∑n=0r∑−1msFHsHH1⋯sHmGE4
where the inner sum is over all pairwise nonisomorphic FG−chains F0F1⋯Fn of length n. However, this is precisely (Eq. (1)). By Theorem 1.14, the right side of (Eq. (4)) is recognizable. Thus the left hand side is recognizable.
Theorem 1.16. Let G be a connected graph with two or more blocks. Then the blocks of G are recognizable.
Proof. First observe that connected graphs with two or more blocks are recognizable. By Theorem 1.9 connectedness is a recognizable property. A connected graph G has two or more blocks if and only if G−v is disconnected for at least one vertex of G, that is, v is a cut-vertex of G. Thus let G be a connected graph with two or more blocks. Then each subgraph F of G that is a block has order less than that of G. Furthermore, for each F0≅F such that VF0⊆VG and EF0⊆EG, there is a unique subgraph H of G that is maximal with respect to the property P2 of being a block (that is, a unique block H of G) such that VF0⊆VH and EF0⊆EH. Therefore by Theorem 1.15, the number mP2FG is the number of blocks of G isomorphic to F.
4. Trees
Paul J. Kelly first proved that trees are reconstructible; but the proof was quite lengthy. Here we present a short proof due to Greenwell and Hemminger using the counting lemma.
A vertex v of a tree G is called a peripheral if it is an end-vertex of a diametrical path of G that is peripheral if its eccentricity ev=diamG. By a branch of a central tree we mean a maximal subtree of G in which the central vertex is an end vertex. A branch of a bicentral tree of G is a maximal subtree of G containing the central edge and in which the central edge is incident with an end vertex. A radial branch is a branch that contains a peripheral vertex of the tree. A tree is called basic if it has exactly two branches, exactly one of which is a path. The branch that is a path is called the stem of the basic tree; the other branch is called the top.
Theorem 1.17. Every tree of order at least 3 is reconstructible.
Proof. First we note that trees are recognizable. Since the order, size and connectedness of a graph G can be determined from its subgraphs G−v,v∈VG, it can be recognized whether a pq graph G is connected and q=p−1, that is, it can be recognized whether G is a tree. Therefore, we assume that G is a tree. If no vertex of G has degree exceeding 2, then G is a path. Hence, paths are reconstructible. Thus, we assume that G is not a path.That is, G has vertices of degree 3 or more. Then a diametrical path of such a tree G necessarily has order less than G. From Theorem 1.14, it follows that the number of paths of various lengths in G is recognizable. This implies that the diameter is a recognizable parameter.
Since the diameter of a tree equals either 2r or 2r−1 according as the tree is central or bicentral, where r is the radius. It further follows that the radius is recognizable and whether G is central or bicentral is recognizable. We have already mentioned that the number of diametrical paths in G recognizable. Now, a vertex u is peripheral if and only if degGu=1 and G−u has fewer paths of length diamG than does G. Hence the number of peripheral vertices is recognizable.
A central tree G with central vertex v has degGv branches, at least two of which are radial, while a bicentral tree has exactly two branches, both of which are radial. A tree (which is not a path) having radius r is basic if and only if it contains no subgraph of Type 1,2,or 3, as shown in Figure 4. The central vertices are drawn as solid circles. In each case, the indicated u-v path is a diametrical path of the original tree: its length is 2r if the subtree is of Type 1 or Type 2 and is 2r−1 if the subtree is of Type 3. The length a and b of the indicated paths satisfy 1≤a≤r−1 and 1≤b≤r−1. The lengths c and d satisfy 1≤c≤r−2 and 1≤d≤r−2. If a non-basic tree contains a subtree of Type 1, 2 or 3 as a proper subtree, then this is recognizable by Theorem 1.14. Thus, in order to show that all nonbasic trees are recognizable, we need only show that a non-basic tree G is recognizable when G itself is of Type 1,2 or 3.
Figure 4.
Nonbasic trees.
A tree G of order p is of Type 1 if and only if it contains a path of length 2r=p−2, one 3−vertex, and the only subgraph G−v with three components is isomorphic to 2Pr∪K1. A tree G of order p is of Type 2 if and only if it contains a path of length 2r=p−3, has exactly two 3−vertices, and in the two subgraphs G−v with three components, the size of any component that is a path at most r−2. Finally, a tree G of order p is of Type 3 if and only if it contains a path of length 2r−1=p−3, has exactly two 3−vertices, and each subgraph G−v with three components is isomorphic to Pr+1∪Pr−1∪K1 or in each such G−v, the size of any component that is a path at most r−2. Thus nonbasic trees of Types 1,2 and 3 are recognizable. Since nonbasic trees are recognizable, basic trees are also recognizable.
Claim:1 Basic trees are reconstructible.
Let G be a central basic tree, and consider those subgraphs G−v which are bicentral(basic) tree. For each such tree G−v, let mv denote the least distance from a vertex of degree 3 or more in G−v to a vertex incident with the central edge of G−v. Among all such numbers mv, let mv1 be one of minimum value. By adding v1 to G−v1 and joining v1 to the end-vertex of the stem of G−v1, the tree G is obtained. Suppose that G is a bicentral basic tree. Consider all those subgraphs G−v which are central(basic) trees. One of these trees, say G−vp, has a vertex of degree greater than 2 closest to the central vertex. By adding vp to Gvp and joining vp to the end-vertex of the stem of G−vp, the tree G is produced.
Claim:2 Nonbasic trees are reconstructible.
Let G be a nonbasic tree. If F is a subtree of G that is maximal with respect to the property P of being a basic tree having the same diameter as G, then we call F a maximal basic subtree of G. Clearly, every subtree of G with property P has order less than that of G and is a subtree of a unique maximal basic subtree of G. So, if such subtrees exist, by Theorem 1.14, the number of maximal basic subtrees of G isomorphic to a given basic subtree F of G having the same diameter as G is recognizable.
We now determine the radial branches of G. If no subtree of G has property P, then each radial branch of G is a path (of length radG) and the number of radial branches equals the number of peripheral vertices in G. If, on the other hand, G has basic subtrees with the same diameter as that of G, then G has radial branches that are not paths. In fact, every maximal basic subtree of G gives rise to such a branch. Let H1,H2,⋯,Ht be nonisomorphic subtrees of G with property P such that every maximal basic subtree F of G is isomorphic to some Hi, 1≤i≤t, and such that mPHiG>0 for i=1,2,⋯,t. For convenience, let mi=mPHiG. For each i, 1≤i≤t, consider a maximal basic subtree F of G that is isomorphic to Hi. The tree F has one radial branch B that is not a path. If G has n peripheral vertices and B contains ki peripheral vertices (of F and hence of G), then B is the top of n−ki maximal basic subtrees of G isomorphic to Hi(namely, one for each of the n−ki stems produced from the other nki peripheral vertices). Thus, the number mi of maximal basic subtrees isomorphic to Hi equals ℓin−ki, where ℓi is the number of radial branches of G isomorphic to B. Therefore, ℓi=mi/n−ki, where mi, ni and ki are recognizable. The number of radial branches of G that are paths equals n−∑i=1tℓiki. Since bicentral nonbasic trees have only radial branches, it follows that such trees are reconstructible. However, we still construct any nonradial branches that may exist if G is a central nonbasic tree. This can be accomplished though, by observing that, in this case, the nonradial branches of G are the nonradial branches of G−v, where.
v is a peripheral vertex of a radial branch containing at least two peripheral vertices,or.
v is a nonperipheral end vertex of a radial branch.
If no vertex v as described in i and ii exist, then all radial branches of G are paths and the nonradical branches of G are the nonradical branches of G−v with the exception of with the exception of one path of length radG−1, in G−v, where v is a peripheral vertex.
We now illustrate some of the ideas involved in the proof of Theorem 1.17 by considering the subgraphs of Figure 5, where Gi=G−vi for some graph G with VG=v1,v2,⋯,v16.
Figure 5.
Deck of a tree.
Clearly, G has order p=16 and, by Theorem 1.3, size q=15. Since G1 and G2, for example, are connected it follows by Theorem 1.9 that G is connected. Therefore, we recognize G as a tree. Hence, by Theorem 1.17 that G is recognizable. Therefore, we now proceed to reconstruct G..
We observe that G has vertices of degree exceeding 2 (since, for example, G1 does) so that G is not a path. Hence a diametrical path of G has order less than that of G, so by determining the lengths of all paths in the subgraphs G−v, the maximum such length is the diameter of G. The maximum is 6 (which occurs in G1, for example) so that diamG=6. Since the diameter of a tree is either 2r or 2r1, where r is the radius of the tree, depending on whether the tree is central or bicentral, it follows that r=radG=3 and that G is a central tree.
In order to calculate the number n of peripheral vertices of G, we first calculate the number of diametrical paths. This can be done with the aid of Kelly’s Lemma, in which F≅P7 and p1=7. We obtain
sP7G=∑v∈VGsP7G−v16−7=459=5
Thus a vertex v1 of G is a peripheral vertex if and only if G−v1 is a tree and G−v1 has fewer than five diametrical paths. The subgraphs G1,G2,G11, and G12 satisfy these criteria so that the number n of peripheral vertices of G is four.
We next determine whether G is a basic or nonbasic (central) tree. Observe that the Type 1 tree of Figure 6 is a subtree of at least one subgraph G−v (in fact, T is a subtree of all Gi,i≠6). Therefore T is a proper subtree of G and G is nonbasic.
Figure 6.
A type 1 subtree of G.
We now determine the radial branches of G. Since every radial branch that is not a path is the top of some maximal basic subtree of G (that is, a subtree of G that is maximal with respect to the property P of being a basic subtree of G and having diameter 6), we begin by finding the maximal basic subtrees of G. By inspecting the graph, we see that only subtrees of G having property P are trees H1,H2 and H3 shown in Figure 7. Therefore every maximal basic subtree of G is isomorphic to one of H1,H2 and H3.
Figure 7.
The basic subtrees of G having diameter 6.
The number mPH1G of maximal basic subtrees of G isomorphic to H1 can be computed with the aid of (Eq. (1)) of Theorem 1.15. By investigating the subgraphs, we see that there is only one H1G−chain (up to isomorphism), namely the trivial chain H1. Thus by (Eq. (1)), mPH1G=−1sH1G, where sH1G is the number of subtrees of G isomorphic to H1. By using Kelly’s lemma with p1=9, we have
sH1G=∑v∈VGsH1G−v16−9=147=2.
Therefore there are two maximal basic subtrees of G isomorphic to H1.
In order to compute mPH2G, we observe that, up to isomorphism, there are two H2G−chains, namely H2 and H2H1, where H1 is shown in Figure 7. By (Eq. (1)),
mPH2G=−10sH2G+−11sH2H1sH1G.
Again using Kelly’s Lemma, we have
sH2G=∑v∈VGsH2G−v16−8=328=4
One observes that sH2H1=2. Also we have already seen that sH1G=2. So mPH2G=4−2.2=0. Therefore there are no maximal basic subtrees of G isomorphic to H2.
In order to compute mPH3G, we observe that, up to isomorphism, there are two H3G−chains, namely H3 and H3H1, where H1 is shown in Figure 7. By (Eq. (1)),
mPH3G=−10sH3G+−11sH3H1sH1G.
Again using Kelly’s Lemma, we have
sH3G=∑v∈VGsH3G−v16−8=168=2
One observes that sH3H1=1 and we have already seen that sH1G=2. So mPH3G=2−2.1=0. Therefore there are no maximal basic subtrees of G isomorphic to H3.
Thus G has exactly two maximal basic subtrees each of which is isomorphic to H1.
If H′ is a maximal basic subtree of G, then H′≅H1 has one non-path radial branch B, and B is isomorphic to the graph shown in Figure 8, where v corresponds to the central vertex of G.
Figure 8.
The unique non-path radial branch of G.
Since B contains two of the four peripheral vertices of G, each radial branch isomorphic to B is the top of 4−2=2 maximal basic subtrees isomorphic to H1. Thus the number ℓ of radial branches isomorphic to B equals 1, since mPH1G=2.
At this point we conclude that G contains exactly one radial branch that is not a path, namely B. All other radial branches of G are necessarily paths. Since the branch B contains two of the four peripheral vertices possessed by G. It follows that each of the remaining two peripheral vertices corresponds to a radial branch that is a path. All radial branches of G have thus been determined, as shown in Figure 9.
Figure 9.
The radial branches of G.
Since the tree constructed thus far has order 12 and G has order 16, G contains nonradial branches. These can be determined by noticing that G1, for example, is obtained by the deletion of a peripheral vertex of G belonging to the radial branch B. Since B is isomorphic to the graph shown in Figure 9 and contains more than one peripheral vertex of G, the nonradial branches of G1 are precisely the nonradial branches of G. Combining this observation with our information in Figure 9, we have constructed the tree G shown in Figure 10.
Figure 10.
The tree G reconstructed.
5. Diameter two or three
In 2003, S. K. Gupta [8] defined three families of simple graphs of diameter two or three and proved that the reconstruction conjecture is true if reconstruction is proved for either these three families. Already the digraph reconstruction conjecture was disproved [9]. So the proof of the reconstruction conjecture depends on any property on graphs that does not hold for digraphs. Since the diameter is one such property of graphs, graph theorists thought that the final proof of the reconstruction conjecture may hold in this line of direction. Gupta’s reduction of the reconstruction conjecture is presented next.
Gupta defined three disjoint families of simple graphs, namely F1,F2 and F3 such that the reconstruction conjecture is true if it true for the families F1,F2 and F3. These families are quite restrictive in that each has diameter two or three. First of all, it is proved that these families F1,F2 and F3 are recognizable by showing that graphs of diameter two are recognizable. The reconstruction conjecture is thus reduced to showing weak reconstructibility for the three families.
Theorem 1.18. If a graph G has diameter greater than three then the diameter of G¯ is less than three.
Proof. Let G be a connected with diameter greater than 3.
Then there exists u,v∈VG such that duv>3. Clearly the graph G¯ will contain the edge uv. In G¯ any vertex different from u and v is adjacent to u or to v or to both since there is no path of length 3 connecting u and v in G.
Let x and y be any two vertices different from u and v. If they have u or v as a common neighbor in G¯, then xuy or xvy is a path connecting them in G¯. Otherwise, they must be adjacent in G¯ since neighbors of u and neighbors of v are not adjacent in G.
Now define.
C1: class of all graphs H such that diamH=diamH¯=2.
C2: class of all graphs H such that diamH=2 and diamH¯>2.
C3: class of all graphs H such that diamH=diamH¯=3.
For i∈0n−2,pvHi is the number of pairs of non-adjacent vertices of H such that, for each pair, there are exactly i paths of length two between the two vertices, and pavHi is the number of pairs of adjacent vertices of H such that, for each pair, there are exactly i paths of length two between the two vertices.
Theorem 1.19. If pvHn−2>0 or pavHn−2>0 then H¯ is disconnected.
Proof. If pvHn−2>0 or pavHn−2>0, then H must contain at least one pair of vertices, say uv, such that there are n−2 paths of length two between u and v, which means vertices u and v are adjacent to all other remaining n−2 vertices of H. Hence, in H¯, no vertices other than u and v are adjacent to them. Therefore, in H¯, either u and v are isolated vertices or they together form a component isomorphic to K2. Thus, H¯ is disconnected.
Theorem 1.20.
a∑i=1npvHij=j+1pvHj+1+n−j+2pvHj∀j∈0n−3
b∑i=1npavHij=j+1pavHj+1+n−j+2pavHj∀j∈0n−3
Proof. (a) Let uv be a pair of vertices in the graph H such that duv=2 and let there be exactly k paths of length two uv1vuv2v…uvkv between u and v. Then, both in H−u and H−v, the pair uv will not appear at all. In each of the k cards H−vi, where i=1,2,…,k, this pair uv appears as having k−1 paths of length two. In the remaining n−k cards, this pair will appear as having k paths of length two.
(b) Proof is similar to Part(a) but taking uv as a pair of adjacent vertices.
Theorem 1.21.ParameterspvHiandpavHiare reconstructible for alli∈0n−2.
Proof. First we prove that the parameters pvHi are reconstructible and that of pavHi follows similarly.
From the given deck of H, the left hand side of Theorem 1.20(a) is known for j∈0n−3. Thus, from Theorem 1.20(a), we have n−2 independent linear equations of n−1 parameters pvH0,pvH1,⋯,pvHn−3 and pvHn−2.
Case 1. Suppose pvHn−2>0.
Now, by Theorem 1.19, H¯ is disconnected. So H¯ and hence H is reconstructible. Then each parameter pvHi (where i∈0n−2) is clearly reconstructible.
Case 2: Suppose pvHn−2=0.
In this case, we have an additional linearly independent equation pvHn−2=0 apart from the n−1 equations stated in Theorem 1.20(a). Now we have n−1 linearly independent equations with n−1 unknowns namely pvH0,pvH1,⋯,pvHn−3 and pvHn−2. The unique solution set of these equations will provide the values of the parameters pvH0,pvH1,⋯,pvHn−2.
Theorem 1.22.Graphs of diameter two are recognizable.
Proof. Graphs of diameter one are precisely complete graphs and so they are recognizable. If diamH≠1 and pvH0= 0, then diamH= 2 since pvHi (where i∈0n−2) is the number of pairs of non-adjacent vertices of H such that, for each pair, there are exactly i paths of length two between the two vertices. If pvH0> 0, then diamH>2.
The number of pairs of vertices of H such that distance between vertices of each pair is greater than two (or pvH0) is reconstructible.
Theorem 1.23. Families C1,C2 and C3 are recognizable.
Proof. Given the deck of some graph H, H=Hii∈1n, we can get the deck of H¯, H′=Hi¯i∈1n. We can recognize whether diamH=1 or not (as complete graphs are recognizable). If diamH≠1 and pvH0=0, then diamH=2. If pvH0>0, then diamH>2. So we can recognize both H and H¯ whether they have diameter equal to one or two or greater than two. So, C1 and C2 are recognizable. We have, if diamH>2 and diamH¯>2 then diamH=3 and diamH¯=3. Also, G∈C3 if and only if diamH>2 and diamH¯>2. Hence C3 is also recognizable.
The next well known result is useful while proving the reduction of the Reconstruction Conjecture.
Theorem 1.24 ([10]). If a graph H has diameter greater than three then the diameter of H¯ is less than three.
Theorem 1.25 ([11]). If a graph H has radius greater than three then the radius of H¯ is less than three.
Theorem 1.26 (Gupta et al. [8]). The Reconstruction Conjecture is true if and only if all graphs H with diamH=2 and all graphs H with diamH=diamH¯=3 are reconstructible.
Proof. The necessity is obvious. For sufficiency, let H be a graph. If H is disconnected, then it is reconstructible. So, we can take that H is connected. If diamH=2 or diamH=diamH¯=3, then H is reconstructible by hypothesis. Hence we may assume that diamH=1 or, by Theorem 1.24, diamH¯≤2. If diamH=1 or diamH¯=1, then H is reconstructible (because graphs with diameter one are precisely complete graphs). Hence we assume diamH¯=2. Now H¯ is reconstructible by assumption. Hence H is reconstructible by Theorem 1.7.
Theorem 1.27.Graphs onnvertices having ann−1-vertex are reconstructible.
Proof. Since the degree sequence of H is reconstructible, we can recognizable whether the graph has a vertex of degree n−1 or not. Therefore the claim of under consideration is recognizable, weakly reconstructible. In a card H−v, where degHv = n−1, annexing a new vertex to H−v and joining it all the vertices of H−v; the graph H in this way is unique. Hence H is reconstructible.
Lemma 1.28.Separable graphsHwith diamH=2 are reconstructible.
Proof. We know that, graphs G with diamH=2 are recognizable. A connected graph is separable if and only if one of its cards is disconnected. Now H has no non-end block, as otherwise H has diameter greater than 2. So all the blocks of H are end-blocks. Hence H has only one cut vertex, say v. Since diamH=2, v must be adjacent to all other vertices of H. Hence H is reconstructible.
Yang Yongzhi [2] proved the following reduction of the Reconstruction Conjecture in 1988. Yongzhi achieved this significant reduction of the RC by proving the reconstructibility of a new class of graphs called P-graphs. Yongzhi observed that reconstructibility of P-graphs turns out to be of great use while shuttling between a graph and its complement in order to reconstruct it.
Figure 11.
A P-graph on 9 vertices.
Definition 1.29.A graphGwithpvertices is aP-graph, if.
there exists only two blocks inGand one of them is an edge (denote it byrxwithdx=1),and
Proof. Since the degree sequence and the number of cut vertices are reconstructible, recognizability of (i) of Definition 1.31 follows immediately. Existence of u as in (ii) of Definition 1.31 is guaranteed by the existence of a connected card obtained by deleting a p−2 vertex in the given deck of G..
Every graph must be contained in one of the following disjoint classes of graphs: disconnected graphs (which are reconstructible); separable graphs without end vertices (which are reconstructible); separable graphs with end vertices; and 2-connected graphs. Yongzhi [12] further divided the class of separable graphs with end vertices into P-graphs and other than P-graphs, and proved that the former class of graphs is reconstructible if all 2-connected graphs are reconstructible. We omit the proof as it is very lengthy.
Theorem 1.31. P-graphs are reconstructible if all 2-connected graphs are reconstructible.
Theorem 1.32. Every connected graph is reconstructible if and only if every 2-connected graph is reconstructible.
Proof. The necessity is obvious. For proving the sufficiency part, assume that all 2-connected graphs are reconstructible. Let G be a separable graph on p (≥12) vertices. If G has no end vertex then G is reconstructible (by Theorem 1.12).
Thus,wecanassume thatGhasanendvertex andap−2−vertexbecause of Theorems1.12and1.7and the hypothesis.E5
We have two subcases.
Case 1. The graph G has at least two end vertices.
NowG¯hasatleasttwop−2−vertices.E6
Let u1 and u2 be two p−2-vertices in G¯. By (Eq. (6)), G¯ has at most two end vertices and (Eq. (5)) now gives that G¯ has either one or two end vertices.
Case 1.1. The graph G¯ has exactly one end vertex, say y..
Now G¯ is a P-graph (as in (i) and (ii) below) and hence G is reconstructible by Theorem 1.31.
(i) If y is not adjacent to ui,i=1,2, then in G¯−y, u1 and u2 are p−2-vertices and hence G¯−y is a block as G¯−y has only p?1 vertices. Hence G¯ is a P-graph.
(ii) If y is adjacent to u1 (say), then in G¯−y, u2 is adjacent to all the vertices hence no vertex other than u2 can be a cut vertex of G¯−y. Also if u2 were a cut vertex of G¯−y, then u1 and all its p−3 neighbors in G¯−y are confined to a single block with p−2 vertices and the only other vertex of G¯−y must be an end vertex adjacent to u2. Thus G¯ has two end vertices, leading to a contradiction. Hence G¯−y has no cut vertex and G¯ is a P-graph.
Case 1.2. The graph G¯ has exactly two endvertices.
Now the bases of the two endvertices in G¯ are different (otherwise G¯ has at most one p−2-vertices, contradicting (Eq. (6))). No vertex other than the bases of the endvertices can have degree p−2. Hence G¯ has at most two p−2-vertices and (Eq. (6)) now gives that has exactly two p−2-vertices, which are the bases of the endvertices. In this case G¯ is clearly recognizable from its degree sequence and is reconstructible by augmenting an end vertex-deleted card G¯−y (by adding a vertex to G¯−y and joining it to a p−3-vertex).
Case 2. The graph G has exactly one end vertex, say y.
If G has more than one p−2-vertex, then G is a P-graph and hence is reconstructible by Theorem 1.31. Hence let G have exactly one p−2-vertex, say w
Case 2.1. The vertices w and y are nonadjacent in G.
Now we can assume that w is a cut vertex of G as otherwise G is a P-graph and hence is reconstructible. So w and q (the base of y) are the only cut vertices of G. Hence G is the union of three subgraphs Bwq (the non-end block containing w and q), Fw (the union of end-blocks containing w) and the end-block By (K2) containing y.
If degq=p−3 then Fw≅K3 (because G has only one end vertex). Consider a 2-vertex deleted card G−z with exactly two end vertices (the deleted 2-vertex cannot be from Bwq as every 2-vertex in Bwq is adjacent to w and q so that no additional end vertex is created). Such a G−z will have an automorphism that interchanges the two end vertices, interchanges the two bases and fixes all other vertices. Hence all augmentations of G−z by introducing a 2-vertex so that the resulting graph has only one end vertex and only one end-block isomorphic to K3 are isomorphic.
If degq≠p−3 then degq<p−3 (because ∣Fw∣≥3). Now in the cards G−v that are connected and have at least one end vertex (cards for which the deleted vertex is not one of w,y and q), the vertices w,y and q are identifiable as the only cut vertex of degree p−3, the only end vertex nonadjacent with w and the base of y respectively. Among these cards G−v, if we choose one, say G1 such that.
w and q are in the same block, and.
the block containing w and q has maximum number of vertices,
then the non-end block of G1 is Bwq. Hence Bwq is known with w and q labeled.
The only end vertex-deleted card in the deck is G−y and its only cut vertex is w. Since Bwq is known with w and q labeled, there is an isomorphism α from Bwq on to a block of G−y such that αw=w. The graph Gα obtained from G−y by adding a vertex and joining it only with αq is a candidate for G. If β is another such isomorphism and Gβ is the corresponding augmented graph, then Gα≅Gβ under the mapping ψ where
Now in G¯, w is the only end vertex and y is the only p−2-vertex and they are not adjacent. Hence G¯ is reconstructible as in Case 2.1. This completes the proof.
“Reconstruction Conjecture for digraphs” is already disproved by Stockmeyer [9]. So a proof for the Reconstruction Conjecture will depend on some property for graphs which does not extend to digraphs. Such properties are called significant properties (from the reconstruction angle) by Stockmeyer. One such property which arises out of distance in complement is given by Theorems 1.7 and 1.24. So far, in digraphs, there is no definition of complement and diameter such that Theorem 1.7 and 1.24 are simultaneously true. So reductions of the Reconstruction Conjecture obtained using the above theorems apply only for graphs and deserve attention. One reduction was proved in the last chapter (Theorem 1.26) by Gupta et al. [8] using Theorems 1.7 and 1.24. Reconstructibility of the subfamilies of 2-connected graphs in the families ℱ1,ℱ2 and ℱ3 are sufficient for the truth of the Reconstruction Conjecture.
Theorem 1.33 ([13]).All 2-connected graphs are reconstructible if and only if all 2-connected graphsGsuch that diamG=2 or diamG= diamG¯=3 are reconstructible.
Proof. The necessity is obvious. For sufficiency, let G be a 2-connected graph. Since graphs of diameter one are precisely complete graphs, this, together with hypothesis, leaves us to reconstruct only 2-connected graphs G of types (a) and (b) below.
a diamG=3 but diamG¯ is different from 3.
If diamG¯>3, then by Theorem 1.24, diamG<3, giving a contradiction. Hence diamG¯=2. Hence G¯ is reconstructible, by Lemma 1.28 if it is separable and by hypothesis otherwise.
b diamG>3.
Now, by Theorem 1.24, diamG¯<3 and so diamG¯=2, since G is connected. Therefore G¯ and hence G is reconstructible by hypothesis.
Theorem 1.34. All graphs are reconstructible if and only if all 2-connected graphs G such that diamG=2 or diamG = diamG¯ = 3 are reconstructible.
Proof. Follows by Theorems 1.32 and 1.33.
6. Radius two
Theorem 1.35.IfGis connected and radG≥3, then radG¯≤2andG¯has no endvertices.
Proof. Let G be a connected graph with radG≥3. Then radG¯≤2. If possible, let G¯ have endvertices. Then G has an n−2-vertex say v. Hence v is adjacent to all but one vertex, say v′ of G. Hence v′ is adjacent to at least one neighbor of v in G (as G is connected). Hence dvw≤2,∀w∈VG. Hence radG≤2, giving a contradiction. This completes the proof.
Theorem 1.36. All 2-connected graphs are reconstructible if and only if all 2-connected graphs G with radG = 2 are reconstructible.
Proof. The necessity is obvious. For sufficiency, let G be any 2-connected graph. It is enough to show that G or G¯ is reconstructible. If radG=1, then G has a vertex adjacent to all other vertices and hence G is reconstructible. If radG=2, then G is reconstructible by hypothesis.
Now let radG≥3. Then radG¯≤2 and G¯ has no endvertices by Theorem 1.35. If radG¯=1, then G¯ is reconstructible as it has a vertex adjacent to all other vertices. When radG¯=2, G¯ is disconnected, separable without end vertices or 2-connected. Therefore G¯ is reconstructible by Theorem 1.11, Theorem 1.28 or the hypothesis.
Theorem 1.37 ([13]). All graphs are reconstructible if and only if all 2-connected graphs G such that radG=2 are reconstructible.
Proof. By Theorem 1.32, we have all graphs are reconstructible if and only if all 2-connected graphs are reconstructible. We also know that all 2-connected graphs are reconstructible if and only if all 2-connected graphs G such that radG = 2.
As 2-connected graphs are recognizable, the families of 2-connected graphs in the hypothesis of Theorems 1.34 and 1.37 are recognizable. Thus, to settle the Reconstruction Conjecture, it is enough to prove that neither of these two families contains a pair of non-isomorphic graphs having the same deck. However, radius of a graph is not yet proved to be reconstructible.
Many classes of blocks which are cartesian, lexicographic or strong products of graphs have been shown to be weakly reconstructible [6, 7]. Several other families of graphs already proved to be reconstructible contain 2-connected graphs. As there are a number of results on the structure of special classes of graphs of diameter 2, they may lead to the reconstruction of more classes of graphs and further narrow down the classes of graphs to be reconstructed to prove the Reconstruction Conjecture. These narrowed down classes must contain counterexamples to the Reconstruction Conjecture if at all there exists one.
\n',keywords:"Reconstruction, Counting Theorem, Tree, Diameter, 2-connected",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/77911.pdf",chapterXML:"https://mts.intechopen.com/source/xml/77911.xml",downloadPdfUrl:"/chapter/pdf-download/77911",previewPdfUrl:"/chapter/pdf-preview/77911",totalDownloads:201,totalViews:0,totalCrossrefCites:0,dateSubmitted:null,dateReviewed:"June 4th 2021",datePrePublished:"August 7th 2021",datePublished:"May 18th 2022",dateFinished:"August 7th 2021",readingETA:"0",abstract:"A graph is reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs. One of the foremost unsolved problems in Graph Theory is the Reconstruction Conjecture, which asserts that every graph G on at least three vertices is reconstructible. In 1980’s, tremendous work was done and many significant results have been produced on the problem and its variations. During the last three decades, work on it has slowed down gradually. P. J. Kelly (1957) first noted that trees are reconstructible; but the proof is quite lengthy. A short proof, due to Greenwell and Hemminger (1973), was given which is based on a simple, but powerful, counting theorem. This chapter deals with the counting theorem and its subsequent applications; also it ends up with a reduction of the Reconstruction Conjecture using distance and connectedness, which may lead to the final solution of the conjecture.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/77911",risUrl:"/chapter/ris/77911",signatures:"Sivaramakrishnan Monikandan",book:{id:"10676",type:"book",title:"Recent Applications in Graph Theory",subtitle:null,fullTitle:"Recent Applications in Graph Theory",slug:"recent-applications-in-graph-theory",publishedDate:"May 18th 2022",bookSignature:"Harun Pirim",coverURL:"https://cdn.intechopen.com/books/images_new/10676.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-83969-527-8",printIsbn:"978-1-83969-526-1",pdfIsbn:"978-1-83969-528-5",isAvailableForWebshopOrdering:!0,editors:[{id:"146092",title:"Dr.",name:"Harun",middleName:null,surname:"Pirim",slug:"harun-pirim",fullName:"Harun Pirim"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"351447",title:"Associate Prof.",name:"Sivaramakrishnan",middleName:null,surname:"Monikandan",fullName:"Sivaramakrishnan Monikandan",slug:"sivaramakrishnan-monikandan",email:"monikandans@gmail.com",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Reconstructible parameters and graphs",level:"1"},{id:"sec_3",title:"3. Counting theorem",level:"1"},{id:"sec_4",title:"4. Trees",level:"1"},{id:"sec_5",title:"5. Diameter two or three",level:"1"},{id:"sec_6",title:"6. Radius two",level:"1"}],chapterReferences:[{id:"B1",body:'P. J. Kelly, On Isometric Transformations, Ph.D. Thesis, University of Wisconsin, 1942'},{id:"B2",body:'S. M. Ulam, A collection of mathematical problems, Wiley Interscience, New York (1960) p. 29'},{id:"B3",body:'P.J. Kelly, A congruence theorem for trees, Pacific J. Math. 7 (1957) 961-968'},{id:"B4",body:'F. Harary, On the reconstruction of a graph from a collection of subgraphs, in: Theory of Graphs and its Applications (M.Fieldler, ed.) Prague, 1964. 47-52; reprinted, Academic Press, New York, 1964'},{id:"B5",body:'J. A. Bondy and R. L. Hemminger, Graph reconstruction - a survey, J. Graph Theory 1 (1977) 227–268'},{id:"B6",body:'J. A. Bondy, A graph reconstructor’s manual, in Surveys in Combinatorics (Proceedings of the 13th British Combinatorics Conference) London Math. Soc., Lecture Note Ser. 166 (1991) 221–252'},{id:"B7",body:'J. Lauri and R. Scapellato, Topics in Graph Automorphisms and Reconstruction, London Math. Soc. Student Texts 54, 2003'},{id:"B8",body:'S. K. Gupta, P. Mangal and V. Paliwal, Some work towards the proof of the reconstruction conjecture, Discrete Math. 272 (2003) 291–296'},{id:"B9",body:'P. K. Stockmeyer, The falsity of the reconstruction conjecture for tournaments, J. Graph Theory 1 (1977) 19-25'},{id:"B10",body:'F.Harary and R.W. Robinson, The diameter of a graph and its complement, American Math. Monthly, 92 (1985), 211-212'},{id:"B11",body:'D.B.West, Introduction to Graph Theory, Second Edition, Prentice-Hall, Inc. 2005'},{id:"B12",body:'Y. Yongzhi, The Reconstruction Conjecture is true if all 2-connected graphs are reconstructible, J. Graph. Theory, 12 (2) (1988), 237-243'},{id:"B13",body:'S. Ramachandran and S. Monikandan, Graph reconstruction conjecture: Reductions using complement, connectivity and distance, Bull. Inst. Combin. Appl. 56 (2009) 103–108'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Sivaramakrishnan Monikandan",address:"monikandans@gmail.com",affiliation:'
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamilnadu, India
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Your manuscript will be sent to Straive, a leader in content solution services, for language copyediting. You will then receive a typeset proof formatted in XML and available online in HTML and PDF to proofread and check for completeness. The first typeset proof of your manuscript is usually available 10 days after its original submission.
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After we receive your proof corrections and a final typeset of the manuscript is approved, your manuscript is sent to our in house DTP department for technical formatting and online publication preparation.
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Additionally, you will be asked to provide a profile picture (face or chest-up portrait photograph) and a short summary of the book which is required for the book cover design.
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6. INVOICE PAYMENT
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The invoice is generally paid by the author, the author’s institution or funder. The payment can be made by credit card from your Author Panel (one will be assigned to you at the beginning of the project), or via bank transfer as indicated on the invoice. We currently accept the following payment options:
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Credit Card
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PayPal
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Bank Transfer
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IntechOpen will help you complete your payment safely and securely, keeping your personal, professional and financial information safe.
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7. ONLINE PUBLICATION, PRINT AND DELIVERY OF THE BOOK
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IntechOpen authors can choose whether to publish their book online only or opt for online and print editions. IntechOpen Compacts, Monographs and Edited Books will be published on www.intechopen.com. If ordered, print copies are delivered by DHL within 12 to 15 working days.
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If you feel that IntechOpen Compacts, Monographs or Edited Books are the right publishing format for your work, please fill out the publishing proposal form. For any specific queries related to the publishing process, or IntechOpen Compacts, Monographs & Edited Books in general, please contact us at book.department@intechopen.com
Please complete the publishing proposal form. The completed form should serve as an overview of your future Compacts, Monograph or Edited Book. Once submitted, your publishing proposal will be sent for evaluation, and a notice of acceptance or rejection will be sent within 10 to 30 working days from the date of submission.
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2. SUBMIT YOUR MANUSCRIPT
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After approval, you will proceed in submitting your full-length manuscript. 50-130 pages for compacts, 130-500 for Monographs & Edited Books.Your full-length manuscript must follow IntechOpen's Author Guidelines and comply with our publishing rules. Once the manuscript is submitted, but before it is forwarded for peer review, it will be screened for plagiarism.
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3. PEER REVIEW RESULTS
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External reviewers will evaluate your manuscript and provide you with their feedback. You may be asked to revise your draft, or parts of your draft, provide additional information and make any other necessary changes according to their comments and suggestions.
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4. ACCEPTANCE AND PRICE QUOTE
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If the manuscript is formally accepted after peer review you will receive a formal Notice of Acceptance, and a price quote.
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The Open Access Publishing Fee of your IntechOpen Compacts, Monograph or Edited Book depends on the volume of the publication and includes: project management, editorial and peer review services, technical editing, language copyediting, cover design and book layout, book promotion and ISBN assignment.
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We will send you your price quote and after it has been accepted (by both the author and the publisher), both parties will sign a Statement of Work binding them to adhere to the agreed upon terms.
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At this step you will also be asked to accept the Copyright Agreement.
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5. LANGUAGE COPYEDITING, TECHNICAL EDITING AND TYPESET PROOF
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Your manuscript will be sent to Straive, a leader in content solution services, for language copyediting. You will then receive a typeset proof formatted in XML and available online in HTML and PDF to proofread and check for completeness. The first typeset proof of your manuscript is usually available 10 days after its original submission.
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After we receive your proof corrections and a final typeset of the manuscript is approved, your manuscript is sent to our in house DTP department for technical formatting and online publication preparation.
\n\n
Additionally, you will be asked to provide a profile picture (face or chest-up portrait photograph) and a short summary of the book which is required for the book cover design.
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6. INVOICE PAYMENT
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The invoice is generally paid by the author, the author’s institution or funder. The payment can be made by credit card from your Author Panel (one will be assigned to you at the beginning of the project), or via bank transfer as indicated on the invoice. We currently accept the following payment options:
\n\n
\n\t
Credit Card
\n\t
PayPal
\n\t
Bank Transfer
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IntechOpen will help you complete your payment safely and securely, keeping your personal, professional and financial information safe.
\n\n
7. ONLINE PUBLICATION, PRINT AND DELIVERY OF THE BOOK
\n\n
IntechOpen authors can choose whether to publish their book online only or opt for online and print editions. IntechOpen Compacts, Monographs and Edited Books will be published on www.intechopen.com. If ordered, print copies are delivered by DHL within 12 to 15 working days.
\n\n
If you feel that IntechOpen Compacts, Monographs or Edited Books are the right publishing format for your work, please fill out the publishing proposal form. For any specific queries related to the publishing process, or IntechOpen Compacts, Monographs & Edited Books in general, please contact us at book.department@intechopen.com
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Proper management of such cases gives them the opportunity to survive and thrive. In this chapter, simplified flowcharts for the initial management of GS, surgical intra-operative decisions and post-operative active follow-up of such cases will be presented and discussed. The first flowchart will discuss how to deal with a GS case from birth till the operative theatre, while the second flowchart will take the lead to guide the surgeon with the available surgical options and how to choose the suitable one for the case. 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Although the etiology is controversial, the main elements in the natural historical emergence of the type I and type IV, which make up the majority of all types, have become clearer. The majority of CCs are diagnosed in childhood. Clinical presentation varies from jaundice in young patients to nonspecific abdominal pain in older, but morbidity increases with complications such as cholangitis, pancreatitis, perforation, hepatitis, liver failure, and malignancy in delayed diagnosed patients. MRCP is considered the current gold standard diagnostic modality that is able to accurately assess biliary anatomy. Although the treatment approach has been formed over the years, it still has not reached the last state. Eventually, the removal of the entire cyst and the reconstruction of the remaining biliary tract to drainage is the current treatment approach. But the dilemma is the way of reconstruction procedure (hepaticoduodenostomy or hepaticojejunostomy). All patients should be followed up for a long period of time, regardless of the surgery method.",book:{id:"8463",slug:"pediatric-surgery-flowcharts-and-clinical-algorithms",title:"Pediatric Surgery, Flowcharts and Clinical Algorithms",fullTitle:"Pediatric Surgery, Flowcharts and Clinical Algorithms"},signatures:"Hasan Özkan Gezer",authors:[{id:"273381",title:"M.D.",name:"Hasan",middleName:"Özkan",surname:"Gezer",slug:"hasan-gezer",fullName:"Hasan Gezer"}]},{id:"44446",title:"Neonatal Pneumonia",slug:"neonatal-pneumonia",totalDownloads:14750,totalCrossrefCites:1,totalDimensionsCites:5,abstract:null,book:{id:"2990",slug:"neonatal-bacterial-infection",title:"Neonatal Bacterial Infection",fullTitle:"Neonatal Bacterial Infection"},signatures:"Friedrich Reiterer",authors:[{id:"152025",title:"Prof.",name:"Friedrich",middleName:null,surname:"Reiterer",slug:"friedrich-reiterer",fullName:"Friedrich Reiterer"}]},{id:"53683",title:"Pre and Postoperative Management of Pediatric Patients with Congenital Heart Diseases",slug:"pre-and-postoperative-management-of-pediatric-patients-with-congenital-heart-diseases",totalDownloads:4889,totalCrossrefCites:1,totalDimensionsCites:1,abstract:"Stabilization during preoperative cardiac surgery especially in neonates has an important role to predict outcome for pediatric congenital heart surgery. We tried to elaborate general guidelines on how to diagnose and some anticipations for emergency treatments tailored by the type of congenital heart disease in neonates. Stabilization consists of medical treatment including emergent prostaglandin institution in some types of duct dependent lesion. The role of interventional catheterization such as patent ductus arteriosus (PDA) stent, balloon pulmonary valvotomy, etc. as modalities for stabilization before surgery was also elaborated. Some general and specific guidelines based on the type of surgeries for postoperative management were also discussed.",book:{id:"5473",slug:"pediatric-and-neonatal-surgery",title:"Pediatric and Neonatal Surgery",fullTitle:"Pediatric and Neonatal Surgery"},signatures:"Eva Miranda Marwali, Beatrice Heineking and Nikolaus A. 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He is also a faculty member in the Molecular Oncology Program. He obtained his MSc and Ph.D. at Oregon State University and Texas Tech University, respectively. He pursued his postdoctoral studies at Rutgers University Medical School and the National Institutes of Health (NIH/NIDDK), USA. His research focuses on biochemistry, biophysics, genetics, molecular biology, and molecular medicine with specialization in the fields of drug design, protein structure-function, protein folding, prions, microRNA, pseudogenes, molecular cancer, epigenetics, metabolites, proteomics, genomics, protein expression, and characterization by spectroscopic and calorimetric methods.",institutionString:"University of Health Sciences",institution:null},{id:"180528",title:"Dr.",name:"Hiroyuki",middleName:null,surname:"Kagechika",slug:"hiroyuki-kagechika",fullName:"Hiroyuki Kagechika",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/180528/images/system/180528.jpg",biography:"Hiroyuki Kagechika received his bachelor’s degree and Ph.D. in Pharmaceutical Sciences from the University of Tokyo, Japan, where he served as an associate professor until 2004. He is currently a professor at the Institute of Biomaterials and Bioengineering (IBB), Tokyo Medical and Dental University (TMDU). From 2010 to 2012, he was the dean of the Graduate School of Biomedical Science. Since 2012, he has served as the vice dean of the Graduate School of Medical and Dental Sciences. He has been the director of the IBB since 2020. Dr. Kagechika’s major research interests are the medicinal chemistry of retinoids, vitamins D/K, and nuclear receptors. He has developed various compounds including a drug for acute promyelocytic leukemia.",institutionString:"Tokyo Medical and Dental University",institution:{name:"Tokyo Medical and Dental University",country:{name:"Japan"}}},{id:"94311",title:"Prof.",name:"Martins",middleName:"Ochubiojo",surname:"Ochubiojo Emeje",slug:"martins-ochubiojo-emeje",fullName:"Martins Ochubiojo Emeje",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/94311/images/system/94311.jpeg",biography:"Martins Emeje obtained a BPharm with distinction from Ahmadu Bello University, Nigeria, and an MPharm and Ph.D. from the University of Nigeria (UNN), where he received the best Ph.D. award and was enlisted as UNN’s “Face of Research.” He established the first nanomedicine center in Nigeria and was the pioneer head of the intellectual property and technology transfer as well as the technology innovation and support center. Prof. Emeje’s several international fellowships include the prestigious Raman fellowship. He has published more than 150 articles and patents. He is also the head of R&D at NIPRD and holds a visiting professor position at Nnamdi Azikiwe University, Nigeria. He has a postgraduate certificate in Project Management from Walden University, Minnesota, as well as a professional teaching certificate and a World Bank certification in Public Procurement. Prof. Emeje was a national chairman of academic pharmacists in Nigeria and the 2021 winner of the May & Baker Nigeria Plc–sponsored prize for professional service in research and innovation.",institutionString:"National Institute for Pharmaceutical Research and Development",institution:{name:"National Institute for Pharmaceutical Research and Development",country:{name:"Nigeria"}}},{id:"268659",title:"Ms.",name:"Xianquan",middleName:null,surname:"Zhan",slug:"xianquan-zhan",fullName:"Xianquan Zhan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/268659/images/8143_n.jpg",biography:"Dr. Zhan received his undergraduate and graduate training in the fields of preventive medicine and epidemiology and statistics at the West China University of Medical Sciences in China during 1989 to 1999. He received his post-doctoral training in oncology and cancer proteomics for two years at the Cancer Research Institute of Human Medical University in China. In 2001, he went to the University of Tennessee Health Science Center (UTHSC) in USA, where he was a post-doctoral researcher and focused on mass spectrometry and cancer proteomics. Then, he was appointed as an Assistant Professor of Neurology, UTHSC in 2005. He moved to the Cleveland Clinic in USA as a Project Scientist/Staff in 2006 where he focused on the studies of eye disease proteomics and biomarkers. He returned to UTHSC as an Assistant Professor of Neurology in the end of 2007, engaging in proteomics and biomarker studies of lung diseases and brain tumors, and initiating the studies of predictive, preventive, and personalized medicine (PPPM) in cancer. In 2010, he was promoted to Associate Professor of Neurology, UTHSC. Currently, he is a Professor at Xiangya Hospital of Central South University in China, Fellow of Royal Society of Medicine (FRSM), the European EPMA National Representative in China, Regular Member of American Association for the Advancement of Science (AAAS), European Cooperation of Science and Technology (e-COST) grant evaluator, Associate Editors of BMC Genomics, BMC Medical Genomics, EPMA Journal, and Frontiers in Endocrinology, Executive Editor-in-Chief of Med One. He has\npublished 116 peer-reviewed research articles, 16 book chapters, 2 books, and 2 US patents. His current main research interest focuses on the studies of cancer proteomics and biomarkers, and the use of modern omics techniques and systems biology for PPPM in cancer, and on the development and use of 2DE-LC/MS for the large-scale study of human proteoforms.",institutionString:null,institution:{name:"Xiangya Hospital Central South University",country:{name:"China"}}},{id:"40482",title:null,name:"Rizwan",middleName:null,surname:"Ahmad",slug:"rizwan-ahmad",fullName:"Rizwan Ahmad",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/40482/images/system/40482.jpeg",biography:"Dr. Rizwan Ahmad is a University Professor and Coordinator, Quality and Development, College of Medicine, Imam Abdulrahman bin Faisal University, Saudi Arabia. Previously, he was Associate Professor of Human Function, Oman Medical College, Oman, and SBS University, Dehradun. Dr. Ahmad completed his education at Aligarh Muslim University, Aligarh. He has published several articles in peer-reviewed journals, chapters, and edited books. His area of specialization is free radical biochemistry and autoimmune diseases.",institutionString:"Imam Abdulrahman Bin Faisal University",institution:{name:"Imam Abdulrahman Bin Faisal University",country:{name:"Saudi Arabia"}}},{id:"41865",title:"Prof.",name:"Farid A.",middleName:null,surname:"Badria",slug:"farid-a.-badria",fullName:"Farid A. Badria",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/41865/images/system/41865.jpg",biography:"Farid A. Badria, Ph.D., is the recipient of several awards, including The World Academy of Sciences (TWAS) Prize for Public Understanding of Science; the World Intellectual Property Organization (WIPO) Gold Medal for best invention; Outstanding Arab Scholar, Kuwait; and the Khwarizmi International Award, Iran. He has 250 publications, 12 books, 20 patents, and several marketed pharmaceutical products to his credit. He continues to lead research projects on developing new therapies for liver, skin disorders, and cancer. Dr. Badria was listed among the world’s top 2% of scientists in medicinal and biomolecular chemistry in 2019 and 2020. He is a member of the Arab Development Fund, Kuwait; International Cell Research Organization–United Nations Educational, Scientific and Cultural Organization (ICRO–UNESCO), Chile; and UNESCO Biotechnology France",institutionString:"Mansoura University",institution:{name:"Mansoura University",country:{name:"Egypt"}}},{id:"329385",title:"Dr.",name:"Rajesh K.",middleName:"Kumar",surname:"Singh",slug:"rajesh-k.-singh",fullName:"Rajesh K. Singh",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/329385/images/system/329385.png",biography:"Dr. Singh received a BPharm (2003) and MPharm (2005) from Panjab University, Chandigarh, India, and a Ph.D. (2013) from Punjab Technical University (PTU), Jalandhar, India. He has more than sixteen years of teaching experience and has supervised numerous postgraduate and Ph.D. students. He has to his credit more than seventy papers in SCI- and SCOPUS-indexed journals, fifty-five conference proceedings, four books, six Best Paper Awards, and five projects from different government agencies. He is currently an editorial board member of eight international journals and a reviewer for more than fifty scientific journals. He received Top Reviewer and Excellent Peer Reviewer Awards from Publons in 2016 and 2017, respectively. He is also on the panel of The International Reviewer for reviewing research proposals for grants from the Royal Society. He also serves as a Publons Academy mentor and Bentham brand ambassador.",institutionString:"Punjab Technical University",institution:{name:"Punjab Technical University",country:{name:"India"}}},{id:"142388",title:"Dr.",name:"Thiago",middleName:"Gomes",surname:"Gomes Heck",slug:"thiago-gomes-heck",fullName:"Thiago Gomes Heck",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/142388/images/7259_n.jpg",biography:null,institutionString:null,institution:{name:"Universidade Regional do Noroeste do Estado do Rio Grande do Sul",country:{name:"Brazil"}}},{id:"336273",title:"Assistant Prof.",name:"Janja",middleName:null,surname:"Zupan",slug:"janja-zupan",fullName:"Janja Zupan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/336273/images/14853_n.jpeg",biography:"Janja Zupan graduated in 2005 at the Department of Clinical Biochemistry (superviser prof. dr. Janja Marc) in the field of genetics of osteoporosis. Since November 2009 she is working as a Teaching Assistant at the Faculty of Pharmacy, Department of Clinical Biochemistry. In 2011 she completed part of her research and PhD work at Institute of Genetics and Molecular Medicine, University of Edinburgh. She finished her PhD entitled The influence of the proinflammatory cytokines on the RANK/RANKL/OPG in bone tissue of osteoporotic and osteoarthritic patients in 2012. From 2014-2016 she worked at the Institute of Biomedical Sciences, University of Aberdeen as a postdoctoral research fellow on UK Arthritis research project where she gained knowledge in mesenchymal stem cells and regenerative medicine. She returned back to University of Ljubljana, Faculty of Pharmacy in 2016. She is currently leading project entitled Mesenchymal stem cells-the keepers of tissue endogenous regenerative capacity facing up to aging of the musculoskeletal system funded by Slovenian Research Agency.",institutionString:null,institution:{name:"University of Ljubljana",country:{name:"Slovenia"}}},{id:"357453",title:"Dr.",name:"Radheshyam",middleName:null,surname:"Maurya",slug:"radheshyam-maurya",fullName:"Radheshyam Maurya",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/357453/images/16535_n.jpg",biography:null,institutionString:null,institution:{name:"University of Hyderabad",country:{name:"India"}}},{id:"418340",title:"Dr.",name:"Jyotirmoi",middleName:null,surname:"Aich",slug:"jyotirmoi-aich",fullName:"Jyotirmoi Aich",position:null,profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y000038Ugi5QAC/Profile_Picture_2022-04-15T07:48:28.png",biography:"Biotechnologist with 15 years of research including 6 years of teaching experience. Demonstrated record of scientific achievements through consistent publication record (H index = 13, with 874 citations) in high impact journals such as Nature Communications, Oncotarget, Annals of Oncology, PNAS, and AJRCCM, etc. Strong research professional with a post-doctorate from ACTREC where I gained experimental oncology experience in clinical settings and a doctorate from IGIB where I gained expertise in asthma pathophysiology. A well-trained biotechnologist with diverse experience on the bench across different research themes ranging from asthma to cancer and other infectious diseases. An individual with a strong commitment and innovative mindset. Have the ability to work on diverse projects such as regenerative and molecular medicine with an overall mindset of improving healthcare.",institutionString:"DY Patil Deemed to Be University",institution:null},{id:"349288",title:"Prof.",name:"Soumya",middleName:null,surname:"Basu",slug:"soumya-basu",fullName:"Soumya Basu",position:null,profilePictureURL:"https://s3.us-east-1.amazonaws.com/intech-files/0033Y000035QxIDQA0/Profile_Picture_2022-04-15T07:47:01.jpg",biography:"Soumya Basu, Ph.D., is currently working as an Associate Professor at Dr. D. Y. Patil Biotechnology and Bioinformatics Institute, Dr. D. Y. Patil Vidyapeeth, Pune, Maharashtra, India. With 16+ years of trans-disciplinary research experience in Drug Design, development, and pre-clinical validation; 20+ research article publications in journals of repute, 9+ years of teaching experience, trained with cross-disciplinary education, Dr. Basu is a life-long learner and always thrives for new challenges.\r\nHer research area is the design and synthesis of small molecule partial agonists of PPAR-γ in lung cancer. She is also using artificial intelligence and deep learning methods to understand the exosomal miRNA’s role in cancer metastasis. Dr. Basu is the recipient of many awards including the Early Career Research Award from the Department of Science and Technology, Govt. of India. She is a reviewer of many journals like Molecular Biology Reports, Frontiers in Oncology, RSC Advances, PLOS ONE, Journal of Biomolecular Structure & Dynamics, Journal of Molecular Graphics and Modelling, etc. She has edited and authored/co-authored 21 journal papers, 3 book chapters, and 15 abstracts. She is a Board of Studies member at her university. She is a life member of 'The Cytometry Society”-in India and 'All India Cell Biology Society”- in India.",institutionString:"Dr. D.Y. Patil Vidyapeeth, Pune",institution:{name:"Dr. D.Y. Patil Vidyapeeth, Pune",country:{name:"India"}}},{id:"354817",title:"Dr.",name:"Anubhab",middleName:null,surname:"Mukherjee",slug:"anubhab-mukherjee",fullName:"Anubhab Mukherjee",position:null,profilePictureURL:"https://intech-files.s3.amazonaws.com/0033Y0000365PbRQAU/ProfilePicture%202022-04-15%2005%3A11%3A18.480",biography:"A former member of Laboratory of Nanomedicine, Brigham and Women’s Hospital, Harvard University, Boston, USA, Dr. Anubhab Mukherjee is an ardent votary of science who strives to make an impact in the lives of those afflicted with cancer and other chronic/acute ailments. He completed his Ph.D. from CSIR-Indian Institute of Chemical Technology, Hyderabad, India, having been skilled with RNAi, liposomal drug delivery, preclinical cell and animal studies. He pursued post-doctoral research at College of Pharmacy, Health Science Center, Texas A & M University and was involved in another postdoctoral research at Department of Translational Neurosciences and Neurotherapeutics, John Wayne Cancer Institute, Santa Monica, California. In 2015, he worked in Harvard-MIT Health Sciences & Technology as a visiting scientist. He has substantial experience in nanotechnology-based formulation development and successfully served various Indian organizations to develop pharmaceuticals and nutraceutical products. He is an inventor in many US patents and an author in many peer-reviewed articles, book chapters and books published in various media of international repute. Dr. Mukherjee is currently serving as Principal Scientist, R&D at Esperer Onco Nutrition (EON) Pvt. Ltd. and heads the Hyderabad R&D center of the organization.",institutionString:"Esperer Onco Nutrition Pvt Ltd.",institution:null},{id:"319365",title:"Assistant Prof.",name:"Manash K.",middleName:null,surname:"Paul",slug:"manash-k.-paul",fullName:"Manash K. Paul",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/319365/images/system/319365.png",biography:"Manash K. Paul is a Principal Investigator and Scientist at the University of California Los Angeles. He has contributed significantly to the fields of stem cell biology, regenerative medicine, and lung cancer. His research focuses on various signaling processes involved in maintaining stem cell homeostasis during the injury-repair process, deciphering lung stem cell niche, pulmonary disease modeling, immuno-oncology, and drug discovery. He is currently investigating the role of extracellular vesicles in premalignant lung cell migration and detecting the metastatic phenotype of lung cancer via machine-learning-based analyses of exosomal signatures. Dr. Paul has published in more than fifty peer-reviewed international journals and is highly cited. He is the recipient of many awards, including the UCLA Vice Chancellor’s award, a senior member of the Institute of Electrical and Electronics Engineers (IEEE), and an editorial board member for several international journals.",institutionString:"University of California Los Angeles",institution:{name:"University of California Los Angeles",country:{name:"United States of America"}}},{id:"311457",title:"Dr.",name:"Júlia",middleName:null,surname:"Scherer Santos",slug:"julia-scherer-santos",fullName:"Júlia Scherer Santos",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/311457/images/system/311457.jpg",biography:"Dr. Júlia Scherer Santos works in the areas of cosmetology, nanotechnology, pharmaceutical technology, beauty, and aesthetics. Dr. Santos also has experience as a professor of graduate courses. Graduated in Pharmacy, specialization in Cosmetology and Cosmeceuticals applied to aesthetics, specialization in Aesthetic and Cosmetic Health, and a doctorate in Pharmaceutical Nanotechnology. Teaching experience in Pharmacy and Aesthetics and Cosmetics courses. She works mainly on the following subjects: nanotechnology, cosmetology, pharmaceutical technology, aesthetics.",institutionString:"Universidade Federal de Juiz de Fora",institution:{name:"Universidade Federal de Juiz de Fora",country:{name:"Brazil"}}},{id:"219081",title:"Dr.",name:"Abdulsamed",middleName:null,surname:"Kükürt",slug:"abdulsamed-kukurt",fullName:"Abdulsamed Kükürt",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/219081/images/system/219081.png",biography:"Dr. Kükürt graduated from Uludağ University in Turkey. He started his academic career as a Research Assistant in the Department of Biochemistry at Kafkas University. In 2019, he completed his Ph.D. program in the Department of Biochemistry at the Institute of Health Sciences. He is currently working at the Department of Biochemistry, Kafkas University. He has 27 published research articles in academic journals, 11 book chapters, and 37 papers. He took part in 10 academic projects. He served as a reviewer for many articles. He still serves as a member of the review board in many academic journals. He is currently working on the protective activity of phenolic compounds in disorders associated with oxidative stress and inflammation.",institutionString:null,institution:{name:"Kafkas University",country:{name:"Turkey"}}},{id:"178366",title:"Dr.",name:"Volkan",middleName:null,surname:"Gelen",slug:"volkan-gelen",fullName:"Volkan Gelen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/178366/images/system/178366.jpg",biography:"Volkan Gelen is a Physiology specialist who received his veterinary degree from Kafkas University in 2011. Between 2011-2015, he worked as an assistant at Atatürk University, Faculty of Veterinary Medicine, Department of Physiology. In 2016, he joined Kafkas University, Faculty of Veterinary Medicine, Department of Physiology as an assistant professor. Dr. Gelen has been engaged in various academic activities at Kafkas University since 2016. There he completed 5 projects and has 3 ongoing projects. He has 60 articles published in scientific journals and 20 poster presentations in scientific congresses. His research interests include physiology, endocrine system, cancer, diabetes, cardiovascular system diseases, and isolated organ bath system studies.",institutionString:"Kafkas University",institution:{name:"Kafkas University",country:{name:"Turkey"}}},{id:"418963",title:"Dr.",name:"Augustine Ododo",middleName:"Augustine",surname:"Osagie",slug:"augustine-ododo-osagie",fullName:"Augustine Ododo Osagie",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/418963/images/16900_n.jpg",biography:"Born into the family of Osagie, a prince of the Benin Kingdom. I am currently an academic in the Department of Medical Biochemistry, University of Benin. Part of the duties are to teach undergraduate students and conduct academic research.",institutionString:null,institution:{name:"University of Benin",country:{name:"Nigeria"}}},{id:"192992",title:"Prof.",name:"Shagufta",middleName:null,surname:"Perveen",slug:"shagufta-perveen",fullName:"Shagufta Perveen",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/192992/images/system/192992.png",biography:"Prof. Shagufta Perveen is a Distinguish Professor in the Department of Pharmacognosy, College of Pharmacy, King Saud University, Riyadh, Saudi Arabia. Dr. Perveen has acted as the principal investigator of major research projects funded by the research unit of King Saud University. She has more than ninety original research papers in peer-reviewed journals of international repute to her credit. She is a fellow member of the Royal Society of Chemistry UK and the American Chemical Society of the United States.",institutionString:"King Saud University",institution:{name:"King Saud University",country:{name:"Saudi Arabia"}}},{id:"49848",title:"Dr.",name:"Wen-Long",middleName:null,surname:"Hu",slug:"wen-long-hu",fullName:"Wen-Long Hu",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/49848/images/system/49848.jpg",biography:"Wen-Long Hu is Chief of the Division of Acupuncture, Department of Chinese Medicine at Kaohsiung Chang Gung Memorial Hospital, as well as an adjunct associate professor at Fooyin University and Kaohsiung Medical University. Wen-Long is President of Taiwan Traditional Chinese Medicine Medical Association. He has 28 years of experience in clinical practice in laser acupuncture therapy and 34 years in acupuncture. He is an invited speaker for lectures and workshops in laser acupuncture at many symposiums held by medical associations. He owns the patent for herbal preparation and producing, and for the supercritical fluid-treated needle. Dr. Hu has published three books, 12 book chapters, and more than 30 papers in reputed journals, besides serving as an editorial board member of repute.",institutionString:"Kaohsiung Chang Gung Memorial Hospital",institution:{name:"Kaohsiung Chang Gung Memorial Hospital",country:{name:"Taiwan"}}},{id:"298472",title:"Prof.",name:"Andrey V.",middleName:null,surname:"Grechko",slug:"andrey-v.-grechko",fullName:"Andrey V. Grechko",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/298472/images/system/298472.png",biography:"Andrey Vyacheslavovich Grechko, Ph.D., Professor, is a Corresponding Member of the Russian Academy of Sciences. He graduated from the Semashko Moscow Medical Institute (Semashko National Research Institute of Public Health) with a degree in Medicine (1998), the Clinical Department of Dermatovenerology (2000), and received a second higher education in Psychology (2009). Professor A.V. Grechko held the position of Сhief Physician of the Central Clinical Hospital in Moscow. He worked as a professor at the faculty and was engaged in scientific research at the Medical University. Starting in 2013, he has been the initiator of the creation of the Federal Scientific and Clinical Center for Intensive Care and Rehabilitology, Moscow, Russian Federation, where he also serves as Director since 2015. He has many years of experience in research and teaching in various fields of medicine, is an author/co-author of more than 200 scientific publications, 13 patents, 15 medical books/chapters, including Chapter in Book «Metabolomics», IntechOpen, 2020 «Metabolomic Discovery of Microbiota Dysfunction as the Cause of Pathology».",institutionString:"Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology",institution:null},{id:"199461",title:"Prof.",name:"Natalia V.",middleName:null,surname:"Beloborodova",slug:"natalia-v.-beloborodova",fullName:"Natalia V. Beloborodova",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/199461/images/system/199461.jpg",biography:'Natalia Vladimirovna Beloborodova was educated at the Pirogov Russian National Research Medical University, with a degree in pediatrics in 1980, a Ph.D. in 1987, and a specialization in Clinical Microbiology from First Moscow State Medical University in 2004. She has been a Professor since 1996. Currently, she is the Head of the Laboratory of Metabolism, a division of the Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology, Moscow, Russian Federation. N.V. Beloborodova has many years of clinical experience in the field of intensive care and surgery. She studies infectious complications and sepsis. She initiated a series of interdisciplinary clinical and experimental studies based on the concept of integrating human metabolism and its microbiota. Her scientific achievements are widely known: she is the recipient of the Marie E. Coates Award \\"Best lecturer-scientist\\" Gustafsson Fund, Karolinska Institutes, Stockholm, Sweden, and the International Sepsis Forum Award, Pasteur Institute, Paris, France (2014), etc. Professor N.V. Beloborodova wrote 210 papers, five books, 10 chapters and has edited four books.',institutionString:"Federal Research and Clinical Center of Intensive Care Medicine and Rehabilitology",institution:null},{id:"354260",title:"Ph.D.",name:"Tércio Elyan",middleName:"Azevedo",surname:"Azevedo Martins",slug:"tercio-elyan-azevedo-martins",fullName:"Tércio Elyan Azevedo Martins",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/354260/images/16241_n.jpg",biography:"Graduated in Pharmacy from the Federal University of Ceará with the modality in Industrial Pharmacy, Specialist in Production and Control of Medicines from the University of São Paulo (USP), Master in Pharmaceuticals and Medicines from the University of São Paulo (USP) and Doctor of Science in the program of Pharmaceuticals and Medicines by the University of São Paulo. Professor at Universidade Paulista (UNIP) in the areas of chemistry, cosmetology and trichology. Assistant Coordinator of the Higher Course in Aesthetic and Cosmetic Technology at Universidade Paulista Campus Chácara Santo Antônio. Experience in the Pharmacy area, with emphasis on Pharmacotechnics, Pharmaceutical Technology, Research and Development of Cosmetics, acting mainly on topics such as cosmetology, antioxidant activity, aesthetics, photoprotection, cyclodextrin and thermal analysis.",institutionString:null,institution:{name:"University of Sao Paulo",country:{name:"Brazil"}}},{id:"334285",title:"Ph.D. Student",name:"Sameer",middleName:"Kumar",surname:"Jagirdar",slug:"sameer-jagirdar",fullName:"Sameer Jagirdar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/334285/images/14691_n.jpg",biography:"I\\'m a graduate student at the center for biosystems science and engineering at the Indian Institute of Science, Bangalore, India. I am interested in studying host-pathogen interactions at the biomaterial interface.",institutionString:null,institution:{name:"Indian Institute of Science Bangalore",country:{name:"India"}}},{id:"329248",title:"Dr.",name:"Md. Faheem",middleName:null,surname:"Haider",slug:"md.-faheem-haider",fullName:"Md. Faheem Haider",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/329248/images/system/329248.jpg",biography:"Dr. Md. Faheem Haider completed his BPharm in 2012 at Integral University, Lucknow, India. In 2014, he completed his MPharm with specialization in Pharmaceutics at Babasaheb Bhimrao Ambedkar University, Lucknow, India. He received his Ph.D. degree from Jamia Hamdard University, New Delhi, India, in 2018. He was selected for the GPAT six times and his best All India Rank was 34. Currently, he is an assistant professor at Integral University. Previously he was an assistant professor at IIMT University, Meerut, India. He has experience teaching DPharm, Pharm.D, BPharm, and MPharm students. He has more than five publications in reputed journals to his credit. Dr. Faheem’s research area is the development and characterization of nanoformulation for the delivery of drugs to various organs.",institutionString:"Integral University",institution:{name:"Integral University",country:{name:"India"}}},{id:"329795",title:"Dr.",name:"Mohd Aftab",middleName:"Aftab",surname:"Siddiqui",slug:"mohd-aftab-siddiqui",fullName:"Mohd Aftab Siddiqui",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/329795/images/system/329795.png",biography:"Dr. Mohd Aftab Siddiqui is an assistant professor in the Faculty of Pharmacy, Integral University, Lucknow, India, where he obtained a Ph.D. in Pharmacology in 2020. He also obtained a BPharm and MPharm from the same university in 2013 and 2015, respectively. His area of research is the pharmacological screening of herbal drugs/natural products in liver cancer and cardiac diseases. He is a member of many professional bodies and has guided many MPharm and PharmD research projects. Dr. Siddiqui has many national and international publications and one German patent to his credit.",institutionString:"Integral University",institution:null},{id:"255360",title:"Dr.",name:"Usama",middleName:null,surname:"Ahmad",slug:"usama-ahmad",fullName:"Usama Ahmad",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/255360/images/system/255360.png",biography:"Dr. Usama Ahmad holds a specialization in Pharmaceutics from Amity University, Lucknow, India. He received his Ph.D. from Integral University, Lucknow, India, with his work titled ‘Development and evaluation of silymarin nanoformulation for hepatic carcinoma’. Currently, he is an Assistant Professor of Pharmaceutics, at the Faculty of Pharmacy, Integral University. He has been teaching PharmD, BPharm, and MPharm students and conducting research in the novel drug delivery domain. From 2013 to 2014 he worked on a research project funded by SERB-DST, Government of India. He has a rich publication record with more than twenty-four original journal articles, two edited books, four book chapters, and several scientific articles to his credit. He is a member of the American Association for Cancer Research, the International Association for the Study of Lung Cancer, and the British Society for Nanomedicine. Dr. Ahmad’s research focus is on the development of nanoformulations to facilitate the delivery of drugs.",institutionString:"Integral University",institution:{name:"Integral University",country:{name:"India"}}},{id:"333824",title:"Dr.",name:"Ahmad Farouk",middleName:null,surname:"Musa",slug:"ahmad-farouk-musa",fullName:"Ahmad Farouk Musa",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/333824/images/22684_n.jpg",biography:"Dato’ Dr Ahmad Farouk Musa\nMD, MMED (Surgery) (Mal), Fellowship in Cardiothoracic Surgery (Monash Health, Aust), Graduate Certificate in Higher Education (Aust), Academy of Medicine (Mal)\n\n\n\nDato’ Dr Ahmad Farouk Musa obtained his Doctor of Medicine from USM in 1992. He then obtained his Master of Medicine in Surgery from the same university in the year 2000 before subspecialising in Cardiothoracic Surgery at Institut Jantung Negara (IJN), Kuala Lumpur from 2002 until 2005. He then completed his Fellowship in Cardiothoracic Surgery at Monash Health, Melbourne, Australia in 2008. He has served in the Malaysian army as a Medical Officer with the rank of Captain upon completing his Internship before joining USM as a trainee lecturer. He is now serving as an academic and researcher at Monash University Malaysia. He is a life-member of the Malaysian Association of Thoracic & Cardiovascular Surgery (MATCVS) and a committee member of the MATCVS Database. He is also a life-member of the College of Surgeons, Academy of Medicine of Malaysia; a life-member of Malaysian Medical Association (MMA), and a life-member of Islamic Medical Association of Malaysia (IMAM). Recently he was appointed as an Interim Chairperson of Examination & Assessment Subcommittee of the UiTM-IJN Cardiothoracic Surgery Postgraduate Program. As an academic, he has published numerous research papers and book chapters. He has also been appointed to review many scientific manuscripts by established journals such as the British Medical Journal (BMJ). He has presented his research works at numerous local and international conferences such as the European Association for Cardiothoracic Surgery (EACTS) and the European Society of Cardiovascular Surgery (ESCVS), to name a few. He has also won many awards for his research presentations at meetings and conferences like the prestigious International Invention, Innovation & Technology Exhibition (ITEX); Design, Research and Innovation Exhibition, the National Conference on Medical Sciences and the Annual Scientific Meetings of the Malaysian Association for Thoracic and Cardiovascular Surgery. He was awarded the Darjah Setia Pangkuan Negeri (DSPN) by the Governor of Penang in July, 2015.",institutionString:null,institution:{name:"Monash University Malaysia",country:{name:"Malaysia"}}},{id:"30568",title:"Prof.",name:"Madhu",middleName:null,surname:"Khullar",slug:"madhu-khullar",fullName:"Madhu Khullar",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/30568/images/system/30568.jpg",biography:"Dr. Madhu Khullar is a Professor of Experimental Medicine and Biotechnology at the Post Graduate Institute of Medical Education and Research, Chandigarh, India. She completed her Post Doctorate in hypertension research at the Henry Ford Hospital, Detroit, USA in 1985. She is an editor and reviewer of several international journals, and a fellow and member of several cardiovascular research societies. Dr. Khullar has a keen research interest in genetics of hypertension, and is currently studying pharmacogenetics of hypertension.",institutionString:"Post Graduate Institute of Medical Education and Research",institution:{name:"Post Graduate Institute of Medical Education and Research",country:{name:"India"}}},{id:"223233",title:"Prof.",name:"Xianquan",middleName:null,surname:"Zhan",slug:"xianquan-zhan",fullName:"Xianquan Zhan",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/223233/images/system/223233.png",biography:"Xianquan Zhan received his MD and Ph.D. in Preventive Medicine at West China University of Medical Sciences. He received his post-doctoral training in oncology and cancer proteomics at the Central South University, China, and the University of Tennessee Health Science Center (UTHSC), USA. He worked at UTHSC and the Cleveland Clinic in 2001–2012 and achieved the rank of associate professor at UTHSC. Currently, he is a full professor at Central South University and Shandong First Medical University, and an advisor to MS/PhD students and postdoctoral fellows. He is also a fellow of the Royal Society of Medicine and European Association for Predictive Preventive Personalized Medicine (EPMA), a national representative of EPMA, and a member of the American Society of Clinical Oncology (ASCO) and the American Association for the Advancement of Sciences (AAAS). He is also the editor in chief of International Journal of Chronic Diseases & Therapy, an associate editor of EPMA Journal, Frontiers in Endocrinology, and BMC Medical Genomics, and a guest editor of Mass Spectrometry Reviews, Frontiers in Endocrinology, EPMA Journal, and Oxidative Medicine and Cellular Longevity. He has published more than 148 articles, 28 book chapters, 6 books, and 2 US patents in the field of clinical proteomics and biomarkers.",institutionString:"Shandong First Medical University",institution:{name:"Affiliated Hospital of Shandong Academy of Medical Sciences",country:{name:"China"}}}]}},subseries:{item:{id:"25",type:"subseries",title:"Evolutionary Computation",keywords:"Genetic Algorithms, Genetic Programming, Evolutionary Programming, Evolution Strategies, Hybrid Algorithms, Bioinspired Metaheuristics, Ant Colony Optimization, Evolutionary Learning, Hyperparameter Optimization",scope:"Evolutionary computing is a paradigm that has grown dramatically in recent years. This group of bio-inspired metaheuristics solves multiple optimization problems by applying the metaphor of natural selection. It so far has solved problems such as resource allocation, routing, schedule planning, and engineering design. Moreover, in the field of machine learning, evolutionary computation has carved out a significant niche both in the generation of learning models and in the automatic design and optimization of hyperparameters in deep learning models. This collection aims to include quality volumes on various topics related to evolutionary algorithms and, alternatively, other metaheuristics of interest inspired by nature. For example, some of the issues of interest could be the following: Advances in evolutionary computation (Genetic algorithms, Genetic programming, Bio-inspired metaheuristics, Hybrid metaheuristics, Parallel ECs); Applications of evolutionary algorithms (Machine learning and Data Mining with EAs, Search-Based Software Engineering, Scheduling, and Planning Applications, Smart Transport Applications, Applications to Games, Image Analysis, Signal Processing and Pattern Recognition, Applications to Sustainability).",coverUrl:"https://cdn.intechopen.com/series_topics/covers/25.jpg",hasOnlineFirst:!1,hasPublishedBooks:!0,annualVolume:11421,editor:{id:"136112",title:"Dr.",name:"Sebastian",middleName:null,surname:"Ventura Soto",slug:"sebastian-ventura-soto",fullName:"Sebastian Ventura Soto",profilePictureURL:"https://mts.intechopen.com/storage/users/136112/images/system/136112.png",biography:"Sebastian Ventura is a Spanish researcher, a full professor with the Department of Computer Science and Numerical Analysis, University of Córdoba. Dr Ventura also holds the positions of Affiliated Professor at Virginia Commonwealth University (Richmond, USA) and Distinguished Adjunct Professor at King Abdulaziz University (Jeddah, Saudi Arabia). Additionally, he is deputy director of the Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI) and heads the Knowledge Discovery and Intelligent Systems Research Laboratory. He has published more than ten books and over 300 articles in journals and scientific conferences. Currently, his work has received over 18,000 citations according to Google Scholar, including more than 2200 citations in 2020. In the last five years, he has published more than 60 papers in international journals indexed in the JCR (around 70% of them belonging to first quartile journals) and he has edited some Springer books “Supervised Descriptive Pattern Mining” (2018), “Multiple Instance Learning - Foundations and Algorithms” (2016), and “Pattern Mining with Evolutionary Algorithms” (2016). He has also been involved in more than 20 research projects supported by the Spanish and Andalusian governments and the European Union. He currently belongs to the editorial board of PeerJ Computer Science, Information Fusion and Engineering Applications of Artificial Intelligence journals, being also associate editor of Applied Computational Intelligence and Soft Computing and IEEE Transactions on Cybernetics. Finally, he is editor-in-chief of Progress in Artificial Intelligence. He is a Senior Member of the IEEE Computer, the IEEE Computational Intelligence, and the IEEE Systems, Man, and Cybernetics Societies, and the Association of Computing Machinery (ACM). Finally, his main research interests include data science, computational intelligence, and their applications.",institutionString:null,institution:{name:"University of Córdoba",institutionURL:null,country:{name:"Spain"}}},editorTwo:null,editorThree:null,series:{id:"14",title:"Artificial Intelligence",doi:"10.5772/intechopen.79920",issn:"2633-1403"},editorialBoard:[{id:"111683",title:"Prof.",name:"Elmer P.",middleName:"P.",surname:"Dadios",slug:"elmer-p.-dadios",fullName:"Elmer P. 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Initial biochemical studies have been exclusively analytic: dissecting, purifying, and examining individual components of a biological system; in the apt words of Efraim Racker (1913 –1991), “Don’t waste clean thinking on dirty enzymes.” Today, however, biochemistry is becoming more agglomerative and comprehensive, setting out to integrate and describe entirely particular biological systems. The ‘big data’ metabolomics can define the complement of small molecules, e.g., in a soil or biofilm sample; proteomics can distinguish all the comprising proteins, e.g., serum; metagenomics can identify all the genes in a complex environment, e.g., the bovine rumen. 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Dr. Blumenberg’s research is focused on the epidermis, expression of keratin genes, transcription profiling, keratinocyte differentiation, inflammatory diseases and cancers, and most recently the effects of the microbiome on the skin. 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In recent years, the application of chemistry to biological molecules has gained significant interest in medicinal and pharmacological studies. This topic will be devoted to understanding the interplay between biomolecules and chemical compounds, their structure and function, and their potential applications in related fields. Being a part of the biochemistry discipline, the ideas and concepts that have emerged from Chemical Biology have affected other related areas. 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Behind these definitions are hidden all the aspects of normal and pathological functioning of all processes that the topic ‘Metabolism’ will cover within the Biochemistry Series. 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Thus proteomics, an area of research that detects all protein forms expressed in an organism, including splice isoforms and post-translational modifications, is more suitable than genomics for a comprehensive understanding of the biochemical processes that govern life. The most common proteomics applications are currently in the clinical field for the identification, in a variety of biological matrices, of biomarkers for diagnosis and therapeutic intervention of disorders. From the comparison of proteomic profiles of control and disease or different physiological states, which may emerge, changes in protein expression can provide new insights into the roles played by some proteins in human pathologies. Understanding how proteins function and interact with each other is another goal of proteomics that makes this approach even more intriguing. Specialized technology and expertise are required to assess the proteome of any biological sample. 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