PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING-Reference-Cited by-同舟云学术

PLANAR, OUTERPLANAR, AND RING GRAPH OF THE COZERO-DIVISOR GRAPH OF A FINITE COMMUTATIVE RING

Published:2012-11-14 Issue:06 Volume:11 Page:1250103
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

AFKHAMI MOJGAN¹²,KHASHYARMANESH KAZEM³²

Affiliation:

1. Department of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran

2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran

3. Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran

Abstract

Let R be a commutative ring with nonzero identity. The cozero-divisor graph of R, denoted by Γ′(R), is a graph with vertex-set W*(R), which is the set of all nonzero and non-unit elements of R, and two distinct vertices a and b in W*(R) are adjacent if and only if a ∉ Rb and b ∉ Ra. In this paper, we characterize all finite commutative rings R such that Γ′(R) is planar, outerplanar or ring graph.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498812501034

Reference10 articles.

1. When a zero-divisor graph is planar or a complete r-partite graph

2. On the Zero-Divisor Graph of a Ring

3. The Zero-Divisor Graph of a Commutative Ring

4. Beck′s Coloring of a Commutative Ring

Cited by 16 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On cozero divisor graphs of ring Zn;COMMUN COMB OPTIM;2024

2. Independent domination polynomial for the cozero divisor graph of the ring of integers modulo n;Discrete Mathematics Letters;2024-04-04

3. On the line graph structure of the cozero-divisor graph of a commutative ring;Indian Journal of Pure and Applied Mathematics;2024-03-16

4. On the genus of reduced cozero-divisor graph of commutative rings;Soft Computing;2022-11-05

5. On the cozero-divisor graphs associated to rings;AKCE International Journal of Graphs and Combinatorics;2022-08-19