Interplay between various graphs on C(X)ρ

• Dey, Amrita ^[1] ; Bag, Sagarmoy ^[2] ; Mandal, Dhananjoy ^[1]
  1. [1] University of Calcutta

     University of Calcutta

     India

     
  2. [2] Bankim Sardar College
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.4995/agt.24688
• Enlaces
  • Texto completo
• Resumen

  • This article focuses on the study of zero-divisor graph Γ(C(X)P), annihilator graph AG(C(X)P) and weakly zero-divisor graph WΓ(C(X)P) on the ring C(X)P of all real-valued functions on a topological space X that are continuous outside a member of an ideal P of closed subsets of X. We establish that if C(X)P properly contains the ring C(X) of real-valued continuous functions on X, then the radius of Γ(C(X)P) is 2 and it is not triangulated. Moreover, in this situation, both Γ(C(X)P) and AG(C(X)P) are not hypertriangulated and the dominating number of AG(C(X)P) is 2. Furthermore, WΓ(C(X)P) fails to be a complete graph under the hypothesis C(X)P⫌C(X). We establish a connection between the complemented-ness of Γ(C(X)P) and the Von-Neumann regularity of C(X)P under the assumption that C(X)P⊇{χ{p}:p∈X}. We realise that any two of these three graphs coincide if and only if |X|=2 and in this case, the graphs are complete bipartite. We also note that the phenomena of WΓ(C(X)P) being triangulated, hypertriangulated and complemented depend solely on the cardinality of X.

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