Search results for: S. R. Nayaka

Authors: S. R. Nayaka, Putta Swamy

Abstract:

Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

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Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

Abstract:

One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

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Authors: Nayaka S.R., Putta Swamy, Purushothama S.

Abstract:

Let G=(V, E) be a graph. A dominating set S in G is a pendant dominating set if < S > contains a pendant vertex. A pendant dominating set of G which intersects every minimum pendant dominating set in G is called a transversal pendant dominating set. The minimum cardinality of a transversal pendant dominating set is called the transversal pendant domination number of G, denoted by γ_tp(G). In this paper, we begin to study this parameter. We calculate γ_tp(G) for some families of graphs. Furthermore, some bounds and relations with other domination parameters are obtained for γ_tp(G).

Keywords: dominating set, pendant dominating set, pendant domination number, transversal pendant dominating set, transversal pendant domination number

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Authors: A. Priyanka, Sunil Kumar Kainoor, Parinitha Nayaka

Abstract:

Introduction: Ever since the ancient times, rape and other sexual offences are considered to be heinous crimes. Rape is not just another word in the dictionary, but it is the most barbaric act of violence committed with sex being the weapon. Rape is among the highest forms of crime experienced by women and children in all sectors of the society. In recent years, there has been an alarming rise in ratio of rape in India. The burden of such crimes on the society is very huge. The venereal diseases are the worst consequence along with unwanted pregnancies. Aims and Objectives: To determine the socio-demographic profile of the survivors of sexual offences reported to Dept. of Forensic Medicine of a South Indian medical college. Material methods: This retrospective study was conducted in the Department of Forensic Medicine of Raichur Institute of Medical Sciences, Raichur, Karnataka, India. Only survivors of sexual offences cases were included in the study group. Examination of all survivors was carried out by doctors of the said Department. Study period is one year six months, January 2015 to June 2016. Results/ case history: In total 140 cases of sexual offences were examined during study period of which the total survivors accounted to 62.85% i.e. 88 cases. Of the 88 survivors, 61 (69.31%) were registered under POCSO Act. The most affected age group of victims was 10-18 years in 59 (67%) cases. 61% were in acquaintance with the assailants, 18% were classmates/ friends, 13% of accused were Family members/ Relatives, 8% were strangers. 85% of the survivors were hailing from rural setup, while 15% were from urban. 60.65% of the survivors were students, 37.7% were doing Coolie/ Agricultural works. Conclusion: Delay in reporting of cases resulted in loss of vital physical evidences as no concrete report could be generated from the forensic lab after examination of specimens thus there should be coordination among doctors, forensic experts and investigating agency. It is worth mentioning that though a large number of cases of sexual offences are reported as rape many among them are consented acts and hence definite evidence of forceful sexual intercourse is lagging.

Keywords: consensual sex, India, POCSO Act- 2012, India, pregnancy, rape, sexual offence

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Authors: Gaurav Kumar Mishra, Sanjeeva Nayaka, Dalip Kumar Upreti

Abstract:

Our nature exhibited presence of a number of unique plants which can be used as indicator of environmental condition of particular place. Lichens are unique plant which has an ability to absorb not only organic, inorganic and metaloties but also absorb radioactive nuclide substances present in the environment. In the present study pyrenocarpous lichens will used as indicator of good forest health in a particular place. The Pyrenocarpous lichens are simple crust forming with black dot like perithecia have few characters for their taxonomical segregation as compared to their foliose and fruticose brethrean. The thallus colour and nature, presence and absence of hypothallus are only few characters of thallus are used to segregate the pyrenocarpous taxa. The fruiting bodies of pyrenolichens i.e. ascocarps are perithecia. The perithecia and the contents found within them posses many important criteria for the segregation of pyrenocarpous lichen taxa. The ascocarp morphology, ascocarp arrangement, the perithecial wall, ascocarp shape and colour, ostiole shape and position, ostiole colour, ascocarp anatomy including type of paraphyses, asci shape and size, ascospores septation, ascospores wall and periphyses are the valuable charcters used for segregation of different pyrenocarpous lichen taxa. India is represented by the occurrence of the 350 species of 44 genera and eleven families. Among the different genera Pyrenula is dominant with 82 species followed by the Porina with 70 species. Recently, systematic of the pyrenocarpous lichens have been revised by American and European lichenologists using phylogenetic methods. Still the taxonomy of pyrenocarpous lichens is in flux and information generated after the completion of this study will play vital role in settlement of the taxonomy of this peculiar group of lichens worldwide. The Indian Himalayan region exhibit rich diversity of pyrenocarpous lichens in India. The western Himalayan region has luxuriance of pyrenocarpous lichens due to its unique topography and climate condition. However, the eastern Himalayan region has rich diversity of pyrenocarpous lichens due to its warmer and moist climate condition. The rich moist and warmer climate in eastern Himalayan region supports forest with dominance of evergreen tree vegetation. The pyrenocarpous lichens communities are good indicator of young and regenerated forest type. The rich diversity of lichens clearly indicates that moist of the forest within the eastern Himalayan region has good health of forest. Due to fast pace of urbanization and other developmental activities will defiantly have adverse effects on the diversity and distribution of pyrenocarpous lichens in different forest type and the present distribution pattern will act as baseline data for carried out future biomonitoring studies in the area.

Keywords: lichen diversity, indicator species, environmental factors, pyrenocarpous

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