Graphs and Combinatorics

, Volume 22, Issue 3, pp 341–350 | Cite as

On the Neighbour-Distinguishing Index of a Graph

  • Keith Edwards
  • Mirko Horňák
  • Mariusz Woźniak


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.


Bipartite Graph Planar Graph Plane Bipartite Graph Regular Bipartite Graph Cycle Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Keith Edwards
    • 1
  • Mirko Horňák
    • 2
  • Mariusz Woźniak
    • 3
  1. 1.Division of Applied ComputingUniversity of DundeeDundeeUK
  2. 2.Institute of MathematicsP. J. Šafárik UniversityKošiceSlovakia
  3. 3.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland

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