### Abstract:

The rings considered in this article are nonzero
commutative with identity which are not fields. Let R be a ring.
We denote the collection of all proper ideals of R by I(R) and the
collection I(R)\{(0)} by I(R)
∗
. Recall that the intersection graph of
ideals of R, denoted by G(R), is an undirected graph whose vertex
set is I(R)
∗ and distinct vertices I, J are adjacent if and only if
I ∩J = (0) 6 . In this article, we consider a subgraph of G(R), denoted
by H(R), whose vertex set is I(R)
∗ and distinct vertices I, J are
adjacent in H(R) if and only if IJ 6= (0). The purpose of this article
is to characterize rings R with at least two maximal ideals such that
H(R) is planar.

### Description:

Vadhel P. Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring I, nonquasilocal case / P. Vadhel , S. Visweswaran // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 1. - Рp.130-143