THE CLIQUE NUMBER OF Γ(Zpn (α))

The zero-divisor graph of a commutative ring with one (say R) is a graph whose vertices are the nonzero zero-divisors of this ring, with two distinct vertices are adjacent in case their product is zero. This graph is denoted by P(R). We study the zero-divisor graph Gamma(Z(p)n(alpha)) where p is a prime number, Zpn. is the set of integers modulo p(n), and Z(p)n (alpha) = {a + bx : a,b is an element of Z(p)n and X-2 = 0}. We find the clique number of Gamma(Z(p)n (alpha)) and the complete subgraphs of Gamma(Z(p)n(alpha)) that achieve this clique number.