Volume 37 • Number 2 • 2014   • The Independence Number of $\Gamma(\mathbb{Z}_{p^{n}}(x))$ Omar A. AbuGhneim, Emad E. AbdAlJawad, Hasan Al-Ezeh Abstract. 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 $\Gamma(R)$. In this paper, we study the structure of the zero-divisor graph $\Gamma(\mathbb{Z}_{p^{n}}(x))$ where p is an odd prime number, $\mathbb{Z}_{p^{n}}$ is the set of integers modulo $p^{n}$, and $\mathbb{Z}_{p^{n}}(x)$ = {$fa+bx : a,b ∉ \mathbb{Z}_{p^{n}}$ and $x2 = 0$}. We find the Independence number of $\Gamma(\mathbb{Z}_{p^{n}}(x))$. 2010 Mathematics Subject Classification: 05C69, 13A99 Full text: PDF