we shall investigate $\gamma(r)$, the zero-divisor graph of a commutative ring $r$ (where $0 \ne 1$). specifically, if $r$ is the given ring, let $\gamma(r) = (v,e)$ with $v = z(r)$ and $e=\{ \{x,y\} | xy=0\}$. we will show elementary properties of $\gamma(r)$ and restrict our attention to graphs with finitely many vertices.