A bound for the distinguishing index of regular graphs

Florian Lehner*, Monika Pilsniak, Marcin Stawiski

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

An edge-colouring of a graph is distinguishing if the only automorphism that 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 K 2 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 κ such that every connected κ-regular graph has a distinguishing edge-colouring with two colours.

Originalspracheenglisch
Aufsatznummer103145
Seitenumfang9
FachzeitschriftEuropean Journal of Combinatorics
Jahrgang89
DOIs
PublikationsstatusVeröffentlicht - Okt 2020

ASJC Scopus subject areas

  • !!Discrete Mathematics and Combinatorics

Fields of Expertise

  • Information, Communication & Computing

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