• BALANCED DOMINATION NUMBER OF A TREE

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, this new parameter is going to be analyzed for trees. If T is a tree with order n 3 and  l leaves, (T)+ l – 1and for s support vertices, (n+s)/2.