A characterization of trees with equal domination and global strong alliance numbers

Abstract

A global strong defensive alliance in a graph G = (V, E) is a dominating set S of G satisfying the condition that for every vertex ∈ S, the number of neighbors v has in S is at least as large as the number of neighbors it has in V - S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in V - S. The global strong alliance number is the minimum cardinality of a global strong defensive alliance in G. We provide a constructive characterization of trees with equal domination and global strong alliance number.