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Proper distinguishing arc-colourings of symmetric digraphs

Author

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  • Kalinowski, Rafał
  • Pilśniak, Monika

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.

Suggested Citation

  • Kalinowski, Rafał & Pilśniak, Monika, 2022. "Proper distinguishing arc-colourings of symmetric digraphs," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s009630032200025x
    DOI: 10.1016/j.amc.2022.126939
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