David Ruelle Zeros of graph-counting polynomials (39K, Plain TeX) ABSTRACT. Given a finite graph $E$ we define a family ${\cal A}$ of subgraphs $F$ by restricting the number of edges of $F$ with endpoint at any vertex of $E$. Defining $Q_{\cal A}(z)=\sum_{F\in {\cal U}}z^{{\rm card}F}$, we can in many cases give precise information on the location of zeros of $Q_{\cal A}(z)$ (zeros all real negative, all imaginary, etc.). Extensions of these results to weighted and infinite graphs are given.