A relationship between global offensive alliance and dominant sets

Abstract

In this paper we show the relationship between global offensive alliance and dominant sets in the graphs and the random graphs. A global offensive alliance in a graph G=(V, E) is a subset S of V such that for every vertex v not in S at least half of the vertices in the closed neighborhood of v are in S and a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is either in D, or has a neighbor in D.