# On the location of roots of the independence polynomial of bounded degree graphs

@inproceedings{Buys2019OnTL, title={On the location of roots of the independence polynomial of bounded degree graphs}, author={Pjotr Buys}, year={2019} }

In [1] Peters and Regts confirmed a conjecture by Sokal by showing that for every $\Delta \in \mathbb{Z}_{\geq 3}$ there exists a complex neighborhood of the interval $\left[0, \frac{\left(\Delta - 1\right)^{\Delta - 1}}{\left(\Delta-2\right)^\Delta}\right)$ on which the independence polynomial is nonzero for all graphs of maximum degree $\Delta$. Furthermore, they gave an explicit neighborhood $U_\Delta$ containing this interval on which the independence polynomial is nonzero for all finite… CONTINUE READING

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