Planar, outerplanar and ring graph of the intersection graph

Author(s):

Soheila Khojasteh *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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:

Intersection graph , Outerplanarity , Planarity , Ring graph

Language:
English
Published:
Journal of Algebraic Structures and Their Applications, Volume:10 Issue: 1, Winter-Spring 2023
Pages:
141 to 149
https://www.magiran.com/p2546158