Prime intersection graph of ideals of a ring

Abstract

Let R be a ring. The prime intersection graph of ideals of R, denoted by $$G_{P}(R)$$ , is the graph whose vertex set is the collection of all non-trivial (left) ideals of R with two distinct vertices I and J are adjacent if and only if $$I\cap J\ne 0$$ and either one of I or J is a prime ideal of R. We discuss connectedness in $$G_{P}(R)$$ . The concepts of bipartition, planarity and colorability are interpreted. Finally, we introduce the idea of traversability in $$G_{P}({\mathbb {Z}}_n)$$ . The core part of this paper is observed in the ring $${\mathbb {Z}}_n$$ .