On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Studies on isolation and molecular characterization of plasmids from Vibrios

While the seriousness of the problem of antibiotic resistance is now recognized, the complex web of resistance linking humans, animals, and the environment is getting realized. More often, antibiotics are used as a preventive measure against diseases. Antibiotic use for agriculture leads to the increased resistance in the environment since antibiotics are inevitable element during agriculture/aquaculture and antibiotic residues are excreted as waste that is frequently spread onto farmland as organic fertilizer. Fecal bacteria survive long periods in the environment and spread through runoff into groundwater, rivers, and marine ecosystems.However, horizontal gene transfer occurs in the animals and guts of humans and in a variety of ecosystems, creating a pool of resistance in the rice fields and open waters. Even if people are not in direct contact with resistant disease through food animals, there are chances of contact with resistant fecal pathogens from the environment. Additionally, pathogens that are autochthonous to the environment can acquire resistance genes from the environment. Our study revealed that autochthonous , bacteria Vibrio spp gained antibiotic resistance in the environment. Further, it was evident that horizontal gene transfer occurs in Vibrio by means of plasmids, which further augments the gravity of the problem. Non-pathogenic bacteria may also acquire resistance genes and serve as a continuing source of resistance for other bacteria, both in the environment, and in the human gut. As the effectiveness of antibiotics for medical applications decline, the indiscriminate use of in aquaculture and in humans can have disastrous conditions in future due to horizontal gene transfer and the spread of resistant organisms: We must recognize and deal with the threat posed by overuse of antibiotics.

Prevalence and Antibiotic sensitivity of Escherichia coli in Extensive Brackish water Aquaculture Ponds

Prevalence and antibiotic resistance of Escherichia coli in the water and sediment samples of brackish water aquaculture ponds adjacent to Cochin backwaters was analysed. More than 50% of the water samples and more than 80% of sediment samples from all the sampling stations were tested positive for £. coli. Risk assessment of the E. coli strains was carried out using multiple antibiotic resistance (MAR) indexing. Majority of the strains were found to be multiple antibiotic resistant suggesting their origin from high risk sources of contamination such as human where antibiotics are frequently used. While none of the £. coli strains were resistant against amikacin, chloramphenicol, streptomycin and trimethoprim, considerable levels of resistance was encountered against ampicillin, erythromycin, penicillin G and vancomycin. High prevalence of £. coli in the water and sediment samples of this extensive brackish water ponds indicates high degree of faecal pollution of this environment. The high risk nature of the strains warrants efficient post harvest and processing measures to avoid health risk to consumers

Evidence Of A Bacilliform Virus Causing Outbreaks Of Whitespot Disease In Penaeus Monodon H. Milne Edwards In India

Whitespot virus could be experimentally transmitted from infected Penoeus monodon to P. in.dicus and repeatedly passed on through several batches of apparently healthy J'. in dieas. During these passages, white spots first disappeared before subsequently reappearing, Electron microscopic studies revealed the presence of oblong-shaped, fully-assembled virus towards the periphery and virus in paracrystalline arrnys towards the center of the hypertrophied nuclei. The virus isolated here is referred to as whitespot syndrome baculovirus (WSBV) until more is known of its antigenic .md genomic rclatodnc..s to isolates from other countries

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

Characterization and Pathogenicity of Vibrio cholerae and Vibrio vulnificus from Marine environments

The genus Vibrioof the family Vibrionaceae are Gram negative, oxidasepositive, rod- or curved- rodshaped facultative anaerobes, widespread in marine and estuarine environments. Vibrio species are opportunistic human pathogens responsible for diarrhoeal disease, gastroenteritis, septicaemia and wound infections and are also pathogens of aquatic organisms, causing infections to crustaceans, bivalves and fishes. In the present study, marine environmental samples like seafood and water and sediment samples from aquafarms and mangroves were screened for the presence of Vibrio species. Of the134 isolates obtained from the various samples, 45 were segregated to the genus Vibrio on the basis of phenotypic characterization.like Gram staining, oxidase test, MoF test and salinity tolerance. Partial 16S rDNA sequence analysis was utilized for species level identification of the isolates and the strains were identified as V. cholerae(N=21), V. vulnificus(N=18), V. parahaemolyticus(N=3), V. alginolyticus (N=2) and V. azureus (N=1). The genetic relatedness and variations among the 45 Vibrio isolates were elucidated based on 16S rDNA sequences. Phenotypic characterization of the isolates was based on their response to 12 biochemical tests namely Voges-Proskauers’s (VP test), arginine dihydrolase , tolerance to 3% NaCl test, ONPG test that detects β-galactosidase activity, and tests for utilization of citrate, ornithine, mannitol, arabinose, sucrose, glucose, salicin and cellobiose. The isolates exhibited diverse biochemical patterns, some specific for the species and others indicative of their environmental source.Antibiogram for the isolates was determined subsequent to testing their susceptibility to 12 antibiotics by the disc diffusion method. Varying degrees of resistance to gentamycin (2.22%), ampicillin(62.22%), nalidixic acid (4.44%), vancomycin (86.66), cefixime (17.77%), rifampicin (20%), tetracycline (42.22%) and chloramphenicol (2.22%) was exhibited. All the isolates were susceptible to streptomycin, co-trimoxazole, trimethoprim and azithromycin. Isolates from all the three marine environments exhibited multiple antibiotic resistance, with high MAR index value. The molecular typing methods such as ERIC PCR and BOX PCR revealed intraspecies relatedness and genetic heterogeneity within the environmental isolatesof V. cholerae and V. vulnificus. The 21 strains of V. choleraewere serogroupedas non O1/ non O139 by screening for the presence O1rfb and O139 rfb marker genes by PCR. The virulence/virulence associated genes namely ctxA, ctxB, ace, VPI, hlyA, ompU, rtxA, toxR, zot, nagst, tcpA, nin and nanwere screened in V. cholerae and V. vulnificusstrains.The V. vulnificusstrains were also screened for three species specific genes viz., cps, vvhand viu. In V. cholerae strains, the virulence associated genes like VPI, hlyA, rtxA, ompU and toxR were confirmed by PCR. All the isolates, except for strain BTOS6, harbored at least one or a combination of the tested genes and V. choleraestrain BTPR5 isolated from prawn hosted the highest number of virulence associated genes. Among the V. vulnificusstrains, only 3 virulence genes, VPI, toxR and cps, were confirmed out of the 16 tested and only 7 of the isolates had these genes in one or more combinations. Strain BTPS6 from aquafarm and strain BTVE4 from mangrove samples yielded positive amplification for the three genes. The toxRgene from 9 strains of V. choleraeand 3 strains of V. vulnificus were cloned and sequenced for phylogenetic analysis based on nucleotide and the amino acid sequences. Multiple sequence alignment of the nucleotide sequences and amino acid sequences of the environmental strains of V. choleraerevealed that the toxRgene in the environmental strains are 100% homologous to themselves and to the V. choleraetoxR gene sequence available in the Genbank database. The 3 strains of V. vulnificus displayed high nucleotide and amino acid sequence similarity among themselves and to the sequences of V. cholerae and V. harveyi obtained from the GenBank database, but exhibited only 72% homology to the sequences of its close relative V. vulnificus. Structure prediction of the ToxR protein of Vibrio cholerae strain BTMA5 was by PHYRE2 software. The deduced amino acid sequence showed maximum resemblance with the structure of DNA-binding domain of response regulator2 from Escherichia coli k-12 Template based homology modelling in PHYRE2 successfully modelled the predicted protein and its secondary structure based on protein data bank (PDB) template c3zq7A. The pathogenicity studies were performed using the nematode Caenorhabditiselegansas a model system. The assessment of pathogenicity of environmental strain of V. choleraewas conducted with E. coli strain OP50 as the food source in control plates, environmental V. cholerae strain BTOS6, negative for all tested virulence genes, to check for the suitability of Vibrio sp. as a food source for the nematode;V. cholerae Co 366 ElTor, a clinical pathogenic strain and V. cholerae strain BTPR5 from seafood (Prawn) and positive for the tested virulence genes like VPI, hlyA, ompU,rtxA and toxR. It was found that V. cholerae strain BTOS6 could serve as a food source in place of E. coli strain OP50 but behavioral aberrations like sluggish movement and lawn avoidance and morphological abnormalities like pharyngeal and intestinal distensions and bagging were exhibited by the worms fed on V. cholerae Co 366 ElTor strain and environmental BTPR5 indicating their pathogenicity to the nematode. Assessment of pathogenicity of the environmental strains of V. vulnificus was performed with V. vulnificus strain BTPS6 which tested positive for 3 virulence genes, namely, cps, toxRand VPI, and V. vulnificus strain BTMM7 that did not possess any of the tested virulence genes. A reduction was observed in the life span of worms fed on environmental strain of V. vulnificusBTMM7 rather than on the ordinary laboratory food source, E. coli OP50. Behavioral abnormalities like sluggish movement, lawn avoidance and bagging were also observed in the worms fed with strain BTPS6, but the pharynx and the intestine were intact. The presence of multi drug resistant environmental Vibrio strainsthat constitute a major reservoir of diverse virulence genes are to be dealt with caution as they play a decisive role in pathogenicity and horizontal gene transfer in the marine environments.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.