Global offensive alliances in some special classes of graphs

Abstract

An offensive alliance in a graph G = (V,E) is a nonempty set of vertices S\subseteq V where for every vertex v in its boundary  N(S)\S, it holds that the majority of vertices in v's closed neighborhood are in S. The offensive alliance number, denoted by a_o(G), is the minimum cardinality of an offensive alliance in G. An alliance S is said to be global if S is a dominating set of G. The global offensive alliance number, denoted by \gamma_{a_o}(G), is the minimum cardinality of a global offensive alliance in G. In this study, we determine some characterizations of a global offensive alliance in some special classes of graphs. Bounds or exact values for the associated invariant are also established.