Document Type : Research Paper

**Author**

Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

**Abstract**

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.

**Keywords**

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February 2023

Pages 141-149