Discrete Mathematics

P_2p-factorization of a complete bipartite graph for an integer was studied by Wang [1]. Further, Beiliang [2] extended the work of Wang [1], and studied the -factorization of complete bipartite multigraphs. For even value of in -factorization, the spectrum problem is completely solved [1, 2, 3]. However for odd value of i.e. and , the path factorization have been studied by a number of researchers [4, 5, 6, 7]. Again, factorizations of complete bipartite multigraphs and symmetric complete bipartite multi-digraphs were studied by Wang and Beiliang[8]. Also, Beiliang and Wang have shown that Ushio conjecture is true for bipartite graphs[9]. In the present paper we shall show that ushio conjecture is also true for factorization of complete bipartite graphs. That is, we shall prove that a necessary and sufficient condition for the existence of a -factorization of is integer.

Total Dominating Color Transversal Set of a graph is a Total Dominating Set which is also Transversal of Some ? - Partition of vertices of G. Here ? is the Chromatic number of the graph G. A Total Dominating Color Transversal Set of a graph G is called Minimal Total Dominating Color Transversal Set of the graph if no proper subset of it is a Total Dominating Color Transversal Set of G. In this paper, we determine a necessary and sufficient condition under which a Total Dominating Color Transversal Set becomes Minimal. We also obtain Minimal Total Dominating Color Transversal set of Generalised Petersen graph P (n, 1).

ABSTRACT A subset D of the vertex set V(G) of a graph G is said to be a dominating set if every vertex not in D is adjacent to at least one vertex in D. A dominating set D is a connected dominating set, if < D > is a connected subgraph of G. For a Connected Graph G, a connected dominating set D is said to be a connected eccentric dominating set if for every v Î V-D, there exists at least one eccentric point of v in D. The minimum of the cardinalities of the connected eccentric dominating sets of G is called the connected eccentric domination number gced(G) of G. In this paper, bounds for g¬ced, and its exact value for some particular classes of graphs are found.

We have given in this paper a fairly decent introduction to the importance of the study of centrality measures of distance graphs. We have discussed at length several concepts with a number of interesting examples and highlighted interesting results. Then, the scope of practical applicability of these concepts is also indicated.

In this paper, the Riemann Zeta function is presented as a function with real and imaginary parts. Thus we are able to evaluate By writing as a bilinear function, and through the use of Sobolev space theorem, an optimization problem with a variable coefficient is derived. Some methods of solution are presented.

The relationship among the turning point, the critical strip and the zeros of Riemann Zeta function is Investigated and established in this paper. A theorem to prove the link between the turning point and the real part of a quadratic function with complex roots is also presented, thereby showing that the real part of the roots will always be the critical point of the quadratic function, thus establishing Riemann’s hypothesis. is shown to be the analytic continuation formula of as presented by Riemann, amidst the various presentations of in his work. A proof of the nature of the zeros is found in this work.

In this paper, we define a new algebraic structure of an anti Q-fuzzy normal HX group and lower level subset of an anti Q-fuzzy normal HX group and discussed some of its properties. We also define anti Q-fuzzy normalizer and establish the relation with anti Q-fuzzy normal HX group. Characterizations of lower level subsets of an anti Q-fuzzy HX subgroup of a HX group are given.

In this work, we make use of the well known product rule and Leibnitz’s theorem to generate a new method which can be used to obtain the higher order derivatives of any functions which depends on four variables. The new method does not require the knowledge of the preceding derivative before obtaining the succeeding ones.

The main objective of the present paper is to establish a summation formula based on half argument in connection with Hypergeometric function.

In this paper the existence of odd and even ratio edge antimagic labeling for double triangular snakes (2?k-snake), 2m?1-snake, 2m?k-snake and kC4-snake are proved.