Nowhere-zero 3-flows in nilpotently vertex-transitive graphs

TL;DR

This paper proves that certain highly symmetric regular graphs with nilpotent automorphism groups always admit a nowhere-zero 3-flow, extending understanding of flow properties in symmetric graph classes.

Contribution

It establishes the existence of nowhere-zero 3-flows in regular graphs with nilpotent vertex-transitive automorphism groups, a new class of graphs for which this property is confirmed.

Findings

Regular graphs of valency at least four with nilpotent vertex-transitive automorphism groups admit nowhere-zero 3-flows.

The proof applies group-theoretic methods to graph flow problems.

Extends known results to a broader class of symmetric graphs.

Abstract

We prove that every regular graph of valency at least four whose automorphism group contains a nilpotent subgroup acting transitively on the vertex set admits a nowhere-zero 3-flow.