  For each nonnegative integer $i$, let $a_i$ be the number of $i$-subsets of
$V(G)$ that induce an acyclic subgraph of a given graph $G$. We define $A(G,x)
= \sum_{i \geq 0} a_i x^i$ (the generating function for $a_i$) to be the
acyclic polynomial for $G$. After presenting some properties of these
polynomials, we investigate the nature and location of their roots.
