On the global offensive alliance number of a graph

Abstract: An offensive alliance in a graph is a set of vertices where for each vertex in its boundary the majority of vertices in ’s closed neighborhood are in . In the case of strong offensive alliance, strict majority is required. An alliance is called global if it affects every vertex in , that is, is a dominating set of . The global offensive alliance number is the minimum cardinality of a global offensive alliance in . An offensive alliance is connected if its induced subgraph is connected. The global-connected offensive alliance number, , is the minimum cardinality of a global-connected offensive alliance in . In this paper we obtain several tight bounds on and in terms of several parameters of . The case of strong alliances is studied by analogy. [Copyright &y& Elsevier]