@article {
author = {Amjadi, J. and khoeilar, R. and Alilou, A.},
title = {The annihilator-inclusion Ideal graph of a commutative ring},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {2},
pages = {231-248},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26752.1139},
abstract = {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.},
keywords = {annihilator,graph,annihilator-inclusion ideal graph},
url = {http://comb-opt.azaruniv.ac.ir/article_14134.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14134_fabb72cabeefd582e42d9da931cd18fe.pdf}
}