Let Γ(V,E) be a simple connected graph with more than one vertex, without loops or multiple edges. A nonempty subset S⊆V is a global offensive alliance if every vertex v∈V−S satisfies that δS(v)≥δS¯(v)+1. The global offensive alliance numberγo(Γ) is defined as the minimum cardinality among all global offensive alliances. Let R be a finite commutative ring with identity. In this paper, we study the global offensive alliance number of the zero-divisor graph Γ(R).
