 98297 David Ruelle
 Zeros of graphcounting polynomials
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Apr 24, 98

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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.
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