Up to a double cover, every regular connected graph is isomorphic to a Schreier graph

TL;DR

This paper proves that any connected, locally finite regular graph can be represented as a double cover of a Schreier graph, linking graph theory with group actions.

Contribution

It establishes that all connected regular graphs are isomorphic to a Schreier graph's double cover, providing a new structural insight.

Findings

Every connected regular graph has a Schreier double cover.

Schreier graphs can represent all connected regular graphs.

Provides a new perspective on graph symmetries and coverings.

Abstract

We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph.