Topological indices of the zero-divisor graph for direct product of integers modulo ring

AIP conference proceedings 2026

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Authors: Nurhabibah, Abdul Gazir Syarifudin, Intan Muchtadi-Alamsyah, Erma Suwastika, Nor Haniza Sarmin, Nur Idayu Alimon, Ghazali Semil Ismail
DOI: 10.1063/5.0308941
Cited by: 0
References: 10

Abstract

Consider a commutative ring M and Δ(M) = (V, E) as its zero-divisor graph. The vertex set V consists of all the zero-divisors of M and u, v ∈ V with u ≠ v are adjacent if uv = 0M where 0M is the zero element of ring M. This study examines the topological indices of Δ(ℤp ×ℤq) and Δ(ℤp × ℤq2). This research was conducted by observing the indices in several examples and then deducing the results for more general cases. The Schultz index of Δ(ℤp × ℤq), the eccentric connectivity index of Δ(ℤp×ℤq2), and the general zeroth-order Randić index of Δ(ℤp × ℤq2) are obtained for any primes p and q.

Fields of Study & Subjects

Graph theory and applications Rings Modules and Algebras Smarandache Functions and Recreational Number Theory

Publication details

Journal / source
AIP conference proceedings
Volume
3326
Pages
030002–030002
Publication date
1 January 2026
Language
EN