A bound for the distinguishing index of regular graphs
Combinatorics
2020-05-11 v2
Abstract
An edge-colouring of a graph is distinguishing, if the only automorphism which preserves the colouring is the identity. It has been conjectured that all but finitely many connected, finite, regular graphs admit a distinguishing edge-colouring with two colours. We show that all such graphs except admit a distinguishing edge-colouring with three colours. This result also extends to infinite, locally finite graphs. Furthermore, we are able to show that there are arbitrary large infinite cardinals such that every connected -regular graph has distinguishing edge-colouring with two colours.
Keywords
Cite
@article{arxiv.1911.11105,
title = {A bound for the distinguishing index of regular graphs},
author = {Florian Lehner and Monika Pilśniak and Marcin Stawiski},
journal= {arXiv preprint arXiv:1911.11105},
year = {2020}
}