On global offensive k-alliances in graphs

Abstract

We investigate the relationship between global offensive k-alliances and some characteristic sets of a graph including r-dependent sets, τdominating sets and standard dominating sets. In addition, we discuss the close relationship that exist among the (global) offensive k i -alliance number of Γ i , i ∈ {1, 2} and the (global) offensive k-alliance number of Γ 1 ×Γ 2 , for some specific values of k. As a consequence of the study, we obtain bounds on the global offensive k-alliance number in terms of several parameters of the graph.