THE SMALL INTERSECTION GRAPH RELATIVE TO MULTIPLICATION MODULES

Let R be a commutative ring and let M be an Rmodule. We define the small intersection graph G(M) of M with all non-small proper submodules of M as vertices and two distinct vertices N, K are adjacent if and only if N ∩ K is a non-small submodule of M. In this article, we investigate the interplay between the graph-theoretic properties of G(M) and algebraic properties of M, where M is a multiplication module.