ON THE COMMUTING GRAPH OF RINGS-Reference-Cited by-同舟云学术

ON THE COMMUTING GRAPH OF RINGS

Published:2011-06 Issue:03 Volume:10 Page:521-527
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

OMIDI G. R.¹²,VATANDOOST E.³

Affiliation:

1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

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

3. Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran

Abstract

Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R\Z(R) and two vertices a and b are adjacent if ab = ba. It has been shown that the diameter of Γ(R)c is less than 3. For a finite ring R we show that the diameter of Γ(R)c is one if and only if R is the non-commutative ring on 4 elements. Also we characterize all rings where the complements of their commuting graphs are planar. Moreover, we identify the commuting graphs of rings of order pi for i = 2, 3 and prime number p.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498811004811

Reference9 articles.

1. On commuting graphs of semisimple rings

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

3. On the zero-divisor graph of a commutative ring

4. The Zero-Divisor Graph of a Commutative Ring

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