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arXiv · 1911.11105

A bound for the distinguishing index of regular graphs

Florian Lehner·Monika Pilśniak·Marcin Stawiski
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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 $K_2$ 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 $\kappa$ such that every connected $\kappa$-regular graph has distinguishing edge-colouring with two colours.

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Florian Lehner, Monika Pilśniak, Marcin Stawiski. 2019-11-25. A bound for the distinguishing index of regular graphs. https://doi.org/10.1016/j.ejc.2020.103145

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