Computing new degree-based topological indices associated with the zero-divisor graphs of finite commutative rings

Karimi, A.; Movahedi, Fateme; Taheri, S. M.

doi:10.47974/JDMSC-1864

Open Access Research Article

Computing new degree-based topological indices associated with the zero-divisor graphs of finite commutative rings

A. KarimiAmir.krm265@gmail.comDepartment of MathematicsFaculty of SciencesGolestan UniversityGorgan, IranView full profile → , ^*Fateme MovahediCorresponding authorf.movahedi@gu.ac.irDepartment of MathematicsFaculty of SciencesGolestan UniversityGorgan, Iran0000-0001-7863-7915View full profile → , S. M. Taherism.taheri@gu.ac.irDepartment of MathematicsFaculty of SciencesGolestan UniversityGorgan, IranView full profile →

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pp. 1–13Vol. 29Issue 1January 2026DOI: 10.47974/JDMSC-1864 Crossmark XML

Received:: 04 Jul 2023
Published Online:: 28 Jul 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1864
Pages:: 1–13

Abstract

Consider a commutative ring ℜ. Let ℨ*(ℜ) denote the set of zero-divisors of ℜ\{0}. A zero-division graph, denoted by Γ(ℜ), is a graph interrelated with the ring ℜ, where the vertex set consists of the elements in ℨ*(ℜ). In this graph, two vertices w1 and w2 are adjacent if and only if their product satisfies w1 w2 = w2 w1 = 0. In a recent research paper, we explore various degree-based topological indices related to Γ(R). Specifically, we investigate the graph structures for the types of commutative rings including ℤζ2, ℤζ3, ℤζ × ℤζ × ℤζ, ℤζ1 ζ2 and ℤζ21 × ℤζ2 where ζ, ζ1 and ζ2 are the primes. This study sheds light on the algebraic properties of these rings and provides insights into their underlying graph structures.

Keywords

Topological index Zero-divisor graph Commutative ring Sombor index

Subject Classifications

05C5005C6905C25

References

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