Structure Of The Nil Graphs For Product Of Rings

Abstract

Let the set of nilpotent elements of the ring R and the n × n matrix ring over R are  Nil(R) and M_n(R) respectively. Here, we have taken a simple, undirected graph. For graph G, the set of vertices and the set of edges are indicated by V(G) and E(G) respectively. In this paper, we study the structure of the nil graph , where and determine the chromatic number of the graph , for different values of m and n.