• BALANCED DOMINATION NUMBER OF SOME GRAPHS

Abstract

Let G=(V,E) be a graph. A Subset D of V is called a dominating set of G if every vertex in V-D is adjacent to atleast one vertex in D. The Domination number γ(G) of  G is the cardinality of the minimum dominating set of G. Let             G = (V, E ) be a graph and let f  be a function that assigns to each vertex of V to a set of values from the set {1,2,.......k} that is,  f: V(G)  → {1,2,.....k} such that for each u, v V(G), f(u ) ≠ f(v), if  u is adjacent to v in G. Then the dominating set D V(G) is called a balanced dominating set if In this paper, we determine the balanced domination number for complete graph, complete  bipartite graph and  wheels.