On the global powerful alliance number of zero-divisor graphs of finite commutative rings

El-Khabchi Y., Bouba E. M., Koç S.

Journal of Algebra and its Applications, cilt.24, sa.3, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 3
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0219498825500896
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: defensive alliance, offensive alliance, Zero-divisor graph
  • Marmara Üniversitesi Adresli: Hayır

Özet

Let Γ = (V, E) be a finite undirected graph without loops or multiple edges. A nonempty set of vertices _S ⊆ V is called powerful alliance if for every vertex u ∈ N[S], |N[u] ∩ S| ≥ |N[u] ∩ S|. A powerful alliance dominating set is called global. The global powerful alliance number γap(Γ) is defined as the minimum cardinality among all global powerful alliances. In this paper, we initiate the study of the global powerful alliance number of zero-divisor graphs Γ(R) with R is a finite commutative ring. Hence, we calculate γap(Γ(R)) for some usual kind of finite rings. As application, we give the global powerful alliance number of all zero-divisor graphs of finite commutative rings of order ≤ 7.