On global offensive alliance in zero-divisor graphs

2021/06/17 by Raúl Juárez Morales, Morales, Raúl Juárez, Gerardo Reyna Hernández +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.2106.09811

arxiv created 2021/06/17 · arxiv updated 2021/06/21

Abstract

Let \G(V,E) be a simple graph without loops nor multiple edges. A nonempty subset S ⊆ V is said a \em global offensive alliance if every vertex v ∈ V- S satisfies that \d_S(v) ≥ \d_S(v)+1. The \em global offensive alliance number \g^o(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 initiate the study of the global offensive alliance number of the zero-divisor graph \G(R).

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