# Micael Toledo: Generalised voltage graphs

Date: 6. 10. 2019

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 8. 10. 2019, od 10h do 12h, Plemljev seminar, Jadranska 19

**Povzetek.**Given a graph

*X*and a group

*G*we may construct a covering graph Cov(X,G) by means of a voltage assignment Z. The graph Cov(

*X,Z*) is called the regular cover of

*X*arising from the voltage graph (

*X,Z*) and admits a semiregular (fixed point free) group of automorphisms isomorphic to

*G*. Every graph

*X*with a semiregular group of automorphism G can be regarded as the regular cover of the quotient graph

*X/G*with an appropriate voltage assignment. The theory of voltage graphs and their associated regular covers has become an important tool in the study of symmetries of graphs. We present a generalised theory of voltage graphs where

*G*is allowed to be an arbitrary group (not necesarilly semiregular).