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 normalΓ‐flows on an orientation of G whenever q is a positive integer and normalΓ 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 paper gives a survey on the results and problems on the study of real zeros of flow polynomials.