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A bound for the distinguishing index of regular graphs
European Journal of Combinatorics ( IF 0.911 ) Pub Date : 2020-05-22 , DOI: 10.1016/j.ejc.2020.103145
Florian Lehner; Monika Pilśniak; Marcin Stawiski

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 K2 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.
更新日期:2020-05-22

 

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