A NOTE ON GLOBAL DOMINATION IN GRAPHS

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex in V - S is adjacent to at least one vertex in S. A global dominating set is a subset S of V which is a dominating set of both G as well as its complement (G) over bar. The domination number (global domination number) gamma(gamma(g)) of G is the minimum cardinality of a dominating set (global dominating set) of G. In this paper we obtain a characterization of bipartite graphs with gamma(g) = gamma + 1. We also characterize unicyclic graphs and bipartite graphs with gamma(g) = alpha(0) + 1, where alpha(0) is the vertex covering number of G.