Abstract
If \(\mathcal{F}\) is a set of subgraphs F of a finite graph E we define a graph-counting polynomial \(p_\mathcal{F}(z)=\sum _{F\in \mathcal{F}}z^{|F|}\) In the present note we consider oriented graphs and discuss some cases where \(\mathcal{F}\) consists of unbranched subgraphs E. We find several situations where something can be said about the location of the zeros of \(p_\mathcal{F}\).
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Ruelle, D. Graph-Counting Polynomials for Oriented Graphs. J Stat Phys 173, 243–248 (2018). https://doi.org/10.1007/s10955-018-2137-3
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DOI: https://doi.org/10.1007/s10955-018-2137-3