Voltage lifts of graphs from a category theory viewpoint

TL;DR

This paper explores the concept of voltage graphs through the lens of category theory, establishing a formal connection via an adjunction between related categories.

Contribution

It introduces a categorical framework for understanding voltage graphs, linking them to group labeled graphs through an adjunction, which is a novel theoretical insight.

Findings

Derived voltage graphs are characterized by an adjunction in category theory.

The categorical perspective unifies different notions of voltage graphs.

Provides a new theoretical foundation for voltage graph analysis.

Abstract

We prove that the notion of a derived voltage graph comes from an adjunction between the category of voltage graphs and a category of group labeled graphs.