A survey on the study of real zeros of flow polynomials

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.