Canadian mathematical bulletin | |
On the Diameter of Unitary Cayley Graphs of Rings | |
Huadong Su1  | |
[1] School of Mathematical and Statistics Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China | |
关键词: unitary Cayley graph; diameter; $k$-good; unit sum number; self-injective ring; | |
DOI : 10.4153/CMB-2016-014-7 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
The unitary Cayley graph of a ring $R$, denoted$Gamma(R)$, is the simple graphdefined on all elements of $R$, and where two vertices $x$ and$y$are adjacent if and only if $x-y$ is a unit in $R$. The largestdistance between all pairs of vertices of a graph $G$ is calledthediameter of $G$, and is denoted by ${m diam}(G)$. It is provedthat for each integer $ngeq1$, there exists a ring $R$ suchthat${m diam}(Gamma(R))=n$. We also show that ${mdiam}(Gamma(R))in {1,2,3,infty}$ for a ring $R$ with $R/J(R)$self-injective and classify all those rings with ${mdiam}(Gamma(R))=1$, 2, 3 and $infty$, respectively.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912050577239ZK.pdf | 21KB | download |