Year: 2012
Author: Yanyan Gao, Gaohua Tang, Jianlong Chen
Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 313–323
Abstract
The commuting graph of an arbitrary ring $R$, denoted by $Γ(R)$, is a graph whose vertices are all non-central elements of $R$, and two distinct vertices $a$ and $b$ are adjacent if and only if $ab = ba$. In this paper, we investigate the connectivity and the diameter of $Γ(Z_n S_3)$. We show that $Γ(Z_n S_3)$ is connected if and only if $n$ is not a prime number. If $Γ(Z_n S_3)$ is connected then diam $(Γ(Z_n S_3)) = 3$, while if $Γ(Z_n S_3)$ is disconnected then every connected component of $Γ(Z_n S_3)$ must be a complete graph with same size, and we completely determine the vertice set of every connected component.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-CMR-19034
Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 313–323
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: group ring commuting graph connected component diameter of a graph.