Spectrum of the Cozero-Divisor Graph Associated to Ring Zn-Reference-Cited by-同舟云学术

Spectrum of the Cozero-Divisor Graph Associated to Ring Zn

Published:2023-10-11 Issue:10 Volume:12 Page:957
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Rashid Mohd¹^ORCID,Alali Amal S.²^ORCID,Ahmed Wasim¹^ORCID,Mozumder Muzibur Rahman¹^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India

2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Abstract

Let R be a commutative ring with identity 1≠0 and let Z(R)′ be the set of all non-unit and non-zero elements of ring R. Γ′(R) denotes the cozero-divisor graph of R and is an undirected graph with vertex set Z(R)′, w∉zR, and z∉wR if and only if two distinct vertices w and z are adjacent, where qR is the ideal generated by the element q in R. In this article, we investigate the signless Laplacian eigenvalues of the graphs Γ′(Zn). We also show that the cozero-divisor graph Γ′(Zp1p2) is a signless Laplacian integral.

Funder

Princess Nourah bint Abdulrahman University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/957/pdf

Reference10 articles.

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4. On signless Laplacian spectrum of zero divisor graphs of the ring Zn;Pirzada;Korean J. Math.,2021

5. Rather, B.A., Pirzada, S., Naikoo, T.A., and Shang, Y. (2021). On Laplacian eigenvalues of the zero-divisor graph associated to the ring of integers modulo n. Mathematics, 9.

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