TY - JOUR
ID - 21472
TI - The central vertices and radius of the regular graph of ideals
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Shaveisi, Farzad
AD - Razi University
Y1 - 2017
PY - 2017
VL - 6
IS - 4
SP - 1
EP - 13
KW - Arc
KW - artinian ring
KW - eccentricity
KW - radius
KW - regular digraph
DO - 10.22108/toc.2017.21472
N2 - 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.
UR - https://toc.ui.ac.ir/article_21472.html
L1 - https://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf
ER -