Prime Graph of the Commutative Ring Zn

Prime graph is a graph associated to rings denoted by PG(R). PG(R)is defined as the graph whose vertices are the elements of the ring R and any twoelements x and y of R are adjacent in PG(R) if and only if xRy = 0 or yRx = 0.In this paper the chromatic number of prime graph of some rings namely Z_n, where n=prod^r _i=1 p^αi _i , are studied.