The Independence Number of Γ((Zpn(x))

The zero-divisor graph of a commutative ring with unity (say R) is a graph whose vertices are the nonzero zero-divisors of this ring, where two distinct vertices are adjacent when their product is zero. This graph is denoted by G(R). In this paper, we study the structure of the zero-divisor graph G(Zpn (x)) where p is an odd prime number, Zpn is the set of integers modulo pn, and Zpn (x) = fa+bx : a;b 2 Zpn and x2 = 0g. We find the Independence number of G(Zpn (x)).