Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286220211201The annihilator-inclusion Ideal graph of a commutative ring2312481413410.22049/cco.2020.26752.1139ENJ.AmjadiAzarbaijan Shahid Madani University0000-0001-9340-4773R.KhoeilarAzarbaijan Shahid Madani University0000-0002-2981-3625A.AlilouJabir Ibn Hayyan research centerJournal Article20200125Let $R$ 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.http://comb-opt.azaruniv.ac.ir/article_14134_fabb72cabeefd582e42d9da931cd18fe.pdf