# Derived voltage graphs come from an adjunction

@inproceedings{Jenvca2020DerivedVG, title={Derived voltage graphs come from an adjunction}, author={Gejza Jenvca}, year={2020} }

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

## References

SHOWING 1-10 OF 15 REFERENCES

### Topological Graph Theory

- MathematicsHandbook of Graph Theory
- 2003

Introduction Voltage Graphs and Covering Spaces Surfaces and Graph Imbeddings Imbedded Voltage Graphs and Current Graphs Map Colorings The Genus of A Group References.

### Generating all graph coverings by permutation voltage assignments

- MathematicsDiscret. Math.
- 1977

### Voltage Graphs

- Mathematics
- 2007

An important theorem of Gross and Tucker [GT2, Theorem 2.2.2] characterises a directed graph E which admits a free action of a group as a skew product. Here we extend this to directed graphs…

### A Note on Constructing Large Cayley Graphs of Given Degree and Diameter by Voltage Assignments

- MathematicsElectron. J. Comb.
- 1998

It is shown that all of the currently known largest graphs of degree $\le 15$ and diameter $\le 10$ have been found by computer search among Cayley graphs of semidirect products of cyclic groups, and all of them can in fact be described as lifts of smaller Cayley graph of cycling groups, with voltages in (other) cyclicgroups.

### Large graphs with small degree and diameter: a voltage assignment approach

- MathematicsAustralas. J Comb.
- 1998

A fairly general upper bound on the diameter of a lift of small base graphs is derived in terms of the properties of the base voltage graph and discussed.

### Lifting Graph Automorphisms by Voltage Assignments

- MathematicsEur. J. Comb.
- 2000

The problem of lifting graph automorphisms along covering projections and the analysis of lifted groups is considered in a purely combinatorial setting and requires careful re-examination of the whole subject to simplification and generalization of several known results.

### Topology and Groupoids

- Mathematics
- 2006

We publicise a proof of the Jordan Curve Theorem which relates it to the Phragmen-Brouwer Property, and whose proof uses the van Kampen theorem for the fundamental groupoid on a set of base points.

### Categorical Logic and Type Theory

- PhilosophyStudies in logic and the foundations of mathematics
- 2001

### ∞-Categories for the Working Mathematician

- Mathematics
- 2018

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,…