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On the Neighbour-Distinguishing Index of a Graph

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Abstract

A proper edge colouring of a graph G is neighbour-distinguishing provided that it distinguishes adjacent vertices by sets of colours of their incident edges. It is proved that for any planar bipartite graph G with Δ(G)≥12 there is a neighbour-distinguishing edge colouring of G using at most Δ(G)+1 colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.

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Authors and Affiliations

  1. Division of Applied Computing, University of Dundee, Dundee, DD1 4HN, UK

    Keith Edwards

  2. Institute of Mathematics, P. J. Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Mirko Horňák

  3. Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland

    Mariusz Woźniak

Authors
  1. Keith Edwards
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  2. Mirko Horňák
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  3. Mariusz Woźniak
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Correspondence to Mariusz Woźniak.

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Edwards, K., Horňák, M. & Woźniak, M. On the Neighbour-Distinguishing Index of a Graph. Graphs and Combinatorics 22, 341–350 (2006). https://doi.org/10.1007/s00373-006-0671-2

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  • DOI: https://doi.org/10.1007/s00373-006-0671-2

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