Papers by Murthy Kellur Bommaiah
Longitudinal studies play a very important role in human life, plant science and social sciences.... more Longitudinal studies play a very important role in human life, plant science and social sciences. In such studies, data are collected from the respondents over a period of time or periodical intervals. Consequently, effective statistical methods/techniques are required for the analysis of such data. Other names given to such studies are th analysis of repeated measurements and growth curves. The main focus of such data analysis is to s by development, aging and other factors such as application of different treatments over a period of time. Such studies typically have unbalanced designs, missing data and time varying covariates and thus not tenable to standard sta methods. This paper gives an overview of literature and important references which lead for further effective studies.
1) jftLVª h la ö Mhö ,yö&33004@99 REGD. NO. D. L.-33004/99 vlk/kj.k EXTRAORDINARY Hkkx I-[k.M 1 P... more 1) jftLVª h la ö Mhö ,yö&33004@99 REGD. NO. D. L.-33004/99 vlk/kj.k EXTRAORDINARY Hkkx I-[k.M 1 PART I-Section 1 iz kf/dkj ls iz dkf'kr PUBLISHED BY AUTHORITY la -54] ubZ fnYyh] 'kq Øokj] iQjojh 28] 2014@iQkYxq u 9] 1935 No. 54] NEW DELHI, FRIDAY, FEBRUARY 28, 2014/PHALGUNA 9, 1935 ǒव× त ǒव× त ǒव× त ǒव× त मं ]ालय मं ]ालय मं ]ालय मं ]ालय ( ( ( (å य å य å य å यय ǒवभाग य ǒवभाग य ǒवभाग य ǒवभाग) ) ) ) सं कã प सं कã प सं कã प सं कã प नई Ǒदã ली नई Ǒदã ली नई Ǒदã ली नई Ǒदã ली, , , , 28 28 28 28 फरवरȣ फरवरȣ फरवरȣ फरवरȣ, , , , 2014 2014 2014 2014 jftLVª h la ö Mhö ,yö&33004@99 REGD. NO. D. L.-33004/99 vlk/kj.k EXTRAORDINARY Hkkx I-[k.M 1 PART I-Section 1 iz kf/dkj ls iz dkf'kr PUBLISHED BY AUTHORITY la -235] ubZ fnYyh] cq /okj] flrEcj 9] 2015@Hkkae 18] 1937
In a graph G = (V, E), A set I ⊆ V is an independent vertex set if no two vertices in I are adjac... more In a graph G = (V, E), A set I ⊆ V is an independent vertex set if no two vertices in I are adjacent. The number of vertices in a maximum independent set in a graph G is the independence number (or vertex independence number) of G and is denoted by β(G). In this paper, we study the maximum independent vertex energy, denoted by E I (G), of a graph G. We are compute the maximum independent energies of complete graph, complete bipartite graph, star graph, cocktail party graph and Friendship graph. Upper and lower bounds for E I (G) are established.
An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the in... more An equitable dominating set D of a graph G = (V, E) is a split equitable dominating set if the induced subgraph hV − Di is a disconnected. The split equitable domination number ϒse(G) of a graph G is the minimum cardinality of a split equitable dominating set. In this paper, we initiate the study of this new parameter and present some bounds and some exact values for ϒse(G). Also Nordhaus−Gaddum type results are obtained.
Let G = (V, E) be a graph with n vertices and with maximum equitable degree ∆_e(G) =∆_e and minim... more Let G = (V, E) be a graph with n vertices and with maximum equitable degree ∆_e(G) =∆_e and minimum equitable degree δ_e(G) = δ_e.Then the Equitable Degree Polynomial of G is denoted by 〖Deg〗_(e )(G, x) and defined as :〖 Deg〗_(e )(G, x) = ∑_(δ_e)^(∆_e)▒〖deg〗_e (G,i ) x^i , where 〖Deg〗_(e )(G, i) is the number of vertices in G of equitable degree i.In this article research, we introduce new graph’s polynomial representation called the equitable degree polynomials, equitable degree polynomial of some standard graphs are obtained, relation with degree polynomial of a graph are found, the sequence equitable degree of a graph is defined and equitable graphic polynomial is introduced. Finally the necessary and sufficient condition for any polynomial to be equitable graphic is established.
Let G = (V,E)be a graph, a set S ⊆ Vis called a dominating set in Gif every vertex in V - S is ... more Let G = (V,E)be a graph, a set S ⊆ Vis called a dominating set in Gif every vertex in V - S is adjacent to a vertex in S. A dominating set S is called a paired dominating set in G if the induces subgraph〈S〉 contains at least one perfect matching. A paired dominating set which intersecting every maximum independent set in G is called an independent transversal paired dominating set in G. The minimum cardinality of an independent transversal paired dominating set is called the independent transversal paired domination number of G, denoted byγitp(G). In this paper, we begin to study this parameter.
A subset of is called an equitable dominating set of a graph if for every vertex , there ex... more A subset of is called an equitable dominating set of a graph if for every vertex , there exists a vertex , such that and . In this paper we introduce the end equitable domination in graphs. Exacts values for some standards graphs are found, relation between this new concept and another domination parameters are obtained, some graph characterization for the graph is established by using this new parameter and bounds for the end equitable domination number are obtained.
For a graph G, let D⊆V (G) be a dominating set of G. If V −D contains a dominating set D1with res... more For a graph G, let D⊆V (G) be a dominating set of G. If V −D contains a dominating set D1with respect to D, then D1is called a complementary (inverse) dominating set of G. The smallest cardinality among all complementary dominating sets of G is called the complementary domination number of G and it is denoted by γc(G).
Thesis Chapters by Murthy Kellur Bommaiah
Graph polynomial is one of the algebraic representations for graph. In this paper, we introduce a... more Graph polynomial is one of the algebraic representations for graph. In this paper, we introduce a new type of graph polynomial called connected neighbourhood polynomial and we defined the connected neighbourhood roots of a graph. The connected neighbourhood polynomial of some standard graphs is obtained and some properties of this polynomial are established. Mathematics Subject Classification (2000): 05C69 • 05E15
An equitable dominating set í µí±í µí± in a graph í µí°ºí µí°º is called independent equitable ... more An equitable dominating set í µí±í µí± in a graph í µí°ºí µí°º is called independent equitable dominating set if the subgraph induced by í µí±í µí± is connected. In this paper we introduce the Independence end equitable domination in graphs. The values of this concept are found for some families of graphs relations with some other domination parameters are presented. Also we define the IED-graph. Necessary and sufficient conditions for any graph to be IED-graph are established. Mathematics Subject Classification (2000): 05C50.
In a graph (,), a subset ⊆ is called a global dominating set of , if is a dominating set of both ... more In a graph (,), a subset ⊆ is called a global dominating set of , if is a dominating set of both and ̅. The global domination number () is the minimum cardinality of a minimal global dominating set in. In this paper, we study the minimum dominating energy, denoted by (), of a graph and minimum double dominating energy of G. We compute the minimum global dominating energies of complete graph, complete bipartite graph, star graph and cocktail party grap h. Upper and lower bounds for () are established.
An equitable dominating set D is said to be an end equitable dominating set of G if D contains al... more An equitable dominating set D is said to be an end equitable dominating set of G if D contains all the end vertices of VVGG.The minimum cardinality of an end equitable dominating set is called the end equitable domination number of G and is denoted by γ GG. In this paper we study the end equitable domination of dragon graph and the line graph of the dragon graph. Also we get the end equitable domination number of the common neighbourhood graph of dragon graph.
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Papers by Murthy Kellur Bommaiah
Thesis Chapters by Murthy Kellur Bommaiah