On the structure of nil graph of a commutative ring

Let R be a commutative ring and N(R) be the set of all nil elements of index two. The nil graph of R denoted by _N(R), is an undirected graph with the vertex set ZN(R) = {x 2 R|xy 2 N(R) for some y in R = R ? {0}}, and any two vertices x and y of ZN(R) are adjacent if and only if xy 2 N(R).In this paper we determine the chromatic number of the nil graph _N(Zpq) , where Zpqis the cyclic group of order pq. Also we study the diameter and girth of _N(Zpq)