Yazd University Algebraic Structures and Their Applications 2382-9761 10 1 2023 02 01 Planar, outerplanar and ring graph of the intersection graph 141 149 2914 10.22034/as.2022.2914 EN Soheila Khojasteh Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran Journal Article 2021 09 29 Let $R$ be a commutative ring and $M$ be an $R$-module. The $M$-intersection graph of ideals of $R$, denoted by $G_M(R)$ is a graph with the vertex set $I(R)^*$, and two distinct vertices $I$ and $J$ are adjacent if and only if $IM\cap JM\neq 0$. In this paper, we study $G_{R/J}(R/I)$, where $I$ and $J$ are ideals of $R$ and $I\subseteq J$. We characterize all ideals $I$ and $J$ for which $G_{R/J}(R/I)$ is planar, outerplanar or ring graph. https://as.yazd.ac.ir/article_2914_b06272db4849b2e860bfd992973617cb.pdf