Proper distinguishing arc-colourings of symmetric digraphs

Rafał Kalinowski and Monika Pilśniak

Applied Mathematics and Computation, 2022, vol. 421, issue C

Abstract: A symmetric digraph G↔ arises from a simple graph G by substituting each edge uv by a pair of opposite arcs uv→,vu→. An arc-colouring c of G↔ is distinguishing if the only automorphism of G↔ preserving c is the identity. We study four types of proper arc-colourings of G↔ corresponding to four definitions of adjacency of arcs. For each type, we investigate the distinguishing chromatic index of G↔, i.e. the least number of colours in a distinguishing proper colouring of G↔. We also determine tight bounds for chromatic indices of G↔, i.e. for the least numbers of colours in each type of proper colourings. Colourings of arcs of a symmetric digraph G↔ are equivalent to colourings of halfedges of the graph G, which have applications in computer science.

Keywords: Automorphism; Symmetry breaking; Distinguishing chromatic index (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s009630032200025x

DOI: 10.1016/j.amc.2022.126939

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