The unit graph of a left Artinian ring

被引：27

作者：

Heydari, F. ^{[1
]}

Nikmehr, M. J. ^{[1
]}

机构：

[1] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran

来源：

ACTA MATHEMATICA HUNGARICA | 2013年 / 139卷 / 1-2期

关键词：

unit graph; connectivity; diameter; girth; Hamiltonian graph; Artinian ring;

D O I：

10.1007/s10474-012-0250-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring with non-zero identity and U(R) be the group of units of R. The unit graph of R, denoted by G(R), is a graph defined on the elements of R, and two distinct vertices r and s are adjacent if and only if r+saU(R). We investigate connectivity, diameter and the girth of the unit graph of a left Artinian ring. Also, by providing an algorithm, we determine when the unit graph of a finite ring is Hamiltonian.

引用

页码：134 / 146

页数：13

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