Predavatelj: Ismael González Yero (University of Cádiz, Španija)

A defensive alliance in a graph G is a set A of vertices with the property that every vertex of A has at most one more neighbor outside of A than it has in A. An offensive alliance is a set B of vertices with the property that every vertex in the neighborhood of B has at least one more neighbor in B than it has outside of B. A set D of vertices of G is a dominating set for G if every vertex not in D is adjacent to at least one vertex of D. A defensive (an offensive) alliance is called global if it is also a dominating set. Several results on (defensive, offensive) alliances in graphs are presented in the talk, emphasizing in the case of global offensive alliances in Cartesian product graphs.