TY - JOUR
T1 - On Commuting Graph of Group Ring $Z_nS_3$
AU - Gao , Yanyan
AU - Tang , Gaohua
AU - Chen , Jianlong
JO - Communications in Mathematical Research 
VL - 4
SP - 313
EP - 323
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19034.html
KW - group ring, commuting graph, connected component, diameter of a
graph.
AB - <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>