On global offensive kk-alliances in graphs

We investigate the relationship between global offensive kk-alliances and some characteristic sets of a graph including rr-dependent sets, ττ-dominating sets and standard dominating sets. In addition, we discuss the close relationships that exist among the (global) offensive kiki-alliance number of Γi,i∈{1,2}Γi,i∈{1,2}, and the (global) offensive kk-alliance number of Γ1×Γ2Γ1×Γ2, for some specific values of kk. As a consequence of the study, we obtain bounds on the global offensive kk-alliance number in terms of several parameters of the graph.