On Global Offensive Alliance in Zero-Divisor Graphs

Raúl Juárez Morales, Gerardo Reyna Hernández, Omar Rosario Cayetano and Jesús Romero Valencia
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Raúl Juárez Morales: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco 39750, Mexico
Gerardo Reyna Hernández: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco 39750, Mexico
Omar Rosario Cayetano: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco 39750, Mexico
Jesús Romero Valencia: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo 39087, Mexico

Mathematics, 2022, vol. 10, issue 3, 1-10

Abstract: 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 δ S ( v ) ≥ δ S ¯ ( v ) + 1 . The global offensive alliance number γ 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 study the global offensive alliance number of the zero-divisor graph Γ ( R ) .

Keywords: offensive alliances; zero-divisor graph; commutative rings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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