Trees with unique minimum global offensive alliance

Abstract

Let G = (V, E) be a simple graph. A non-empty set D ⊆ V is called a global offensive alliance if D is a dominating set and for every vertex ν in V − D, |NG [ν] ∩ D|≥|NG [ν] − D|. The global offensive alliance number is the minimum cardinality of a global offensive alliance in G. In this paper, we give a constructive characterization of trees having a unique minimum global offensive alliance.