@Article{CMR-28-313,
author = {Gao , YanyanTang , Gaohua and Chen , Jianlong},
title = {On Commuting Graph of Group Ring $Z_nS_3$},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {28},
number = {4},
pages = {313--323},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2707-8523},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cmr/19034.html}
}