Prime intersection graph of ideals of a ring

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 boolean AND J not equal 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)(Z(n)). The core part of this paper is observed in the ring Z(n).