Some Results on Intersection Graphs of Ideals of Commutative Rings

Abstract

The rings considered in this article are commutative with identity which
admit at least one nonzero proper ideal. Let $R$ be a ring. Recall that the intersection graph of ideals of $R$, denoted by $G(R)$, is an undirected simple graph whose vertex set is the set of all nontrivial ideals of $R$ (an ideal $I$ of $R$ is said to be nontrivial if $I\notin {\{(0),R}\})$ and distinct vertices $I,J$ are joined by an edge in $G(R)$ if and only if $I \cap J\,\, \ne (0)$. Let $r \in \mathbb{N}$. The aim of this article is to characterize rings $R$ such that $G(R)$ is either bipartite or 3-partite.