ON THE REDUCED INTERSECTION GRAPH OF A RING Z_n

Abstract

Abstract: For the ring integers modulo Z_n, we define the Reduced Intersection Graph G^* (Z_n), is a simple undirected graph, whose vertex set is the nonzero ideals of Z_n and two distinct ideals I and J are adjacent if and only if they have nonzero intersection, i.e., I∩J≠∅. In this paper, we investigate the connectedness of the graph G^* (Z_n). Also, we compute the radius, diameter, girth and also domination number of the reduced intersection graph. Further, we compare these parameters for the existed Intersection graph G^' (Z_n) and the reduced intersection graph G^* (Z_n).