%0 Journal Article
%T The central vertices and radius of the regular graph of ideals
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Shaveisi, Farzad
%D 2017
%\ 12/01/2017
%V 6
%N 4
%P 1-13
%! The central vertices and radius of the regular graph of ideals
%K Arc
%K artinian ring
%K eccentricity
%K radius
%K regular digraph
%R 10.22108/toc.2017.21472
%X 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.
%U https://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf