Some properties of intersection graph of a module with an application of the graph of DOUBLE-STRUCK CAPITAL Zn

Let R be an unital ring which is not necessarily commutative. The intersection graph of ideals of R is a graph with the vertex set which contains proper ideals of R and distinct two vertices I and J are adjacent if and only if I c J (1) 0 is denoted by G. In this paper, we will give some properties of regular graph, triangle-free graph and clique number of G(M) for a module M. We also characterize girth of an Artinian module with connected module. We characterize the chromatic number of G(Z (n) ). We also give an algorithm for the chromatic number of G(Z (n) ).