On global offensive -alliances in graphs

We investigate the relationship between global offensive k -alliances and some characteristic sets of a graph including r -dependent sets, τ -dominating sets and standard dominating sets. In addition, we discuss the close relationships 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.