A survey on the study of real zeros of flow polynomials

DOI10.1002/JGT.22458zbMATH Open1443.05083arXiv2007.05195OpenAlexW2920804268WikidataQ128223635 ScholiaQ128223635MaRDI QIDQ3299211

F. M. Dong

Publication date: 17 July 2020

Published in: Journal of Graph Theory (Search for Journal in Brave)

Abstract: For a bridgeless graph $G$, its flow polynomial is defined to be the function $F(G,q)$ which counts the number of nonwhere-zero $Gamma$-flows on an orientation of $G$ whenever $q$ is a positive integer and $Gamma$ is an additive Abelian group of order $q$. It was introduced by Tutte in 1950 and the locations of zeros of this polynomial have been studied by many researchers. This article gives a survey on the results and problems on the study of real zeros of flow polynomials.

Full work available at URL: https://arxiv.org/abs/2007.05195

zbMATH Keywords

bridgeless graphflow polynomialzero-free intervalnowhere-zero flowflow root

Mathematics Subject Classification ID

Graph polynomials (05C31) Enumeration in graph theory (05C30) Flows in graphs (05C21)

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