Generalised Voltage Graphs

TL;DR

This paper extends the theory of voltage graphs to include graphs with non-semiregular automorphism groups, broadening the applicability of derived cover techniques in symmetric graph analysis.

Contribution

It generalizes the classical voltage graph theory to encompass graphs with arbitrary automorphism groups, not just semiregular ones.

Findings

Generalized voltage graph theory to non-semiregular automorphism groups

Extended classical results to broader symmetry settings

Enhanced tools for studying symmetric graphs

Abstract

A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of graphs with a significant degree of symmetry. We generalise this theory to graphs with a group of automorphisms that is not necessarily semiregular, and we generalise several well-known results of the classical theory of voltage graphs to this broader setting.