%0 Journal Article
%T The annihilator-inclusion Ideal graph of a commutative ring
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Amjadi, J.
%A khoeilar, R.
%A Alilou, A.
%D 2021
%\ 12/01/2021
%V 6
%N 2
%P 231-248
%! The annihilator-inclusion Ideal graph of a commutative ring
%K annihilator
%K graph
%K annihilator-inclusion ideal graph
%R 10.22049/cco.2020.26752.1139
%X 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.
%U http://comb-opt.azaruniv.ac.ir/article_14134_fabb72cabeefd582e42d9da931cd18fe.pdf