The central vertices and radius of the regular graph of ideals‎

Document Type : Research Paper


Razi University


The regular graph of ideals of the commutative ring $R$‎, ‎denoted by ${\Gamma_{reg}}(R)$‎, ‎is a graph whose vertex‎ ‎set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element‎. ‎In this paper‎, ‎it is proved that the radius of $\Gamma_{reg}(R)$ equals $3$‎. ‎The central vertices of $\Gamma_{reg}(R)$ are determined‎, ‎too‎.


Main Subjects

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Volume 6, Issue 4 - Serial Number 4
December 2017
Pages 1-13
  • Receive Date: 17 October 2016
  • Revise Date: 01 May 2017
  • Accept Date: 13 May 2017
  • Published Online: 01 December 2017