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On Global Offensive Alliance in Zero-Divisor Graphs

Author

Listed:
  • 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)

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 ) .

Suggested Citation

  • Raúl Juárez Morales & Gerardo Reyna Hernández & Omar Rosario Cayetano & Jesús Romero Valencia, 2022. "On Global Offensive Alliance in Zero-Divisor Graphs," Mathematics, MDPI, vol. 10(3), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:298-:d:728043
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