planar, outerplanar and ring graph of the intersection graph

Let r be a commutative ring and m be an r-module. the m-intersection graph of ideals of r, denoted by gm(r) is a graph with the vertex set i(r) ∗, and two distinct vertices i and j are adjacent if and only if im ∩ jm ̸= 0. in this paper, we study gr/j (r/i), where i and j are ideals of r and i ⊆ j. we characterize all ideals i and j for which gr/j (r/i) is planar, outerplanar or ring graph.