On global offensive k-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 relationship that exist among the (global) offensive ki-alliance number of Γi, i ∈ {1, 2} and the (global) offensive k-alliance number of Γ1×Γ2, 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. e-mail:[email protected]. Partially supported by Ministerio de Ciencia y Tecnoloǵıa, ref. BFM2003-00034 and Junta de Andalućıa, ref. FQM-260 and ref. P06-FQM-02225. e-mail:[email protected]. Partially supported by the Spanish Ministry of Education through projects TSI2007-65406-C03-01 “E-AEGIS” and CONSOLIDER CSD2007-00004 “ARES” and by the Rovira i Virgili University through project 2006AIRE-09 e-mail:[email protected] e-mail: [email protected]