TY - JOUR
ID - 14134
TI - The annihilator-inclusion Ideal graph of a commutative ring
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Amjadi, J.
AU - khoeilar, R.
AU - Alilou, A.
AD - Azarbaijan Shahid Madani University
AD - Jabir Ibn Hayyan research center
Y1 - 2021
PY - 2021
VL - 6
IS - 2
SP - 231
EP - 248
KW - annihilator
KW - graph
KW - annihilator-inclusion ideal graph
DO - 10.22049/cco.2020.26752.1139
N2 - Let $R$ be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of $R$, denoted by $xi_R$, is a graph whose vertex set is the of all non-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either ${rm Ann}(I)subseteq J$ or ${rm Ann}(J)subseteq I$. The purpose of this paper is to provide some basic properties of the graph $xi_R$. In particular, shows that $xi_R$ is a connected graph with diameter at most three, and has girth 3 or $infty$. Furthermore, is determined all isomorphic classes of non-local Artinian rings whose annihilator-inclusion ideal graphs have genus zero or one.
UR - http://comb-opt.azaruniv.ac.ir/article_14134.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14134_fabb72cabeefd582e42d9da931cd18fe.pdf
ER -