ISSN: 2319-8753 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 2, Issue 11, November 2013 Copyright to IJIRSET www.ijirset.com 6419 Degree Equitable Domination Number and Independent Domination Number of a Graph A.Nellai Murugan 1 , G.Victor Emmanuel 2 Assoc. Prof. of Mathematics, V.O. Chidambaram College, Thuthukudi-628 008, Tamilnadu, India 1 Asst. Prof. of Mathematics, St. Mother Theresa Engineering College, Thuthukudi-628 102, Tamilnadu, India 2 Abstract: In this paper, we introduce the degree equitable domination number in graphs. Some interesting relationships are identified between domination and degree equitable domination and independent domination. It is also shown that any positive integers with are realizable as the domination number, degree equitable domination number and independent domination number of a graph. We also investigate the degree equitable domination in the corona of graphs. Mathematics Subject Classification: 05C69 Keywords: Degree equitable dominating set, degree equitable domination number, I. INTRODUCTION The concept of domination in graphs evolved from a chess board problem known as the Queen problem- to find the minimum number of queens needed on an 8x8 chess board such that each square is either occupied or attacked by a queen. C.Berge[3] in 1958 and 1962 and O.Ore[8] in 1962 started the formal study on the theory of dominating sets. Thereafter several studies have been dedicated in obtaining variations of the concept. The authors in [7] listed over 1200 papers related to domination in graphs in over 75 variation. Throughout this paper, G(V, E) a finite, simple, connected and undirected graph where V denotes its vertex set and E its edge set. Unless otherwise stated the graph G has n vertices and m edges. Degree of a vertex v is denoted by d(v), the maximum degree of a graph G is denoted by (G). Let C n a cycle on n vertices, P n a path on n vertices and a complete graph on n vertices by K n . A graph is connected if any two vertices are connected by a path. A maximal connected subgraph of a graph G is called a component of G .The number of components of G is denoted by (G). The complement of G is the graph with vertex set V in which two vertices are adjacent iff they are not adjacent in G. A tree is a connected acyclic graph. A bipartite graph is a graph whose vertex set can be divided into two disjoint sets V 1 and another in V 2 . A complete bipartite graph is a bipartite graph with partitions of order = m and = n, is denoted by K m,n . A star denoted by K 1,n-1 is a tree with one root vertex and n-1 pendant vertices. A bistar, denoted by B(m, n) is the graph obtained by joining the root vertices of the stars denoted by F n can be constructed by identifying n copies of the cycle C 3 at a common vertex. A wheel graph denoted by W n is a graph with n vertices formed by connecting a single vertex to all vertices of C n-1. A Helm graph denoted by H n is a graph obtained from the wheel W n by attaching a pendant vertex to each vertex in the outer cycle of W n . The chromatic number of a graph G denoted by (G) is the smallest number of colors needed to colour all the vertices of a graph G in which adjacent vertices receive different colours . For any real number x, denotes the largest integer greater than or equal to x. A Nordhaus- G addum – type result is a lower or upper bound on the sum or product of a parameter of a graph and its complement. Throughout this paper, we only consider undirected graphs with no loops .The basic definitions and concepts used in this study are adopted from[11].