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On the neighbour-distinguishing index of a graph. (English) Zbl 1107.05032
Summary: 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 $$\Delta(G) \geq 12$$ there is a neighbour-distinguishing edge colouring of $$G$$ using at most $$\Delta(G)+1$$ colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.
Reviewer: Reviewer (Berlin)

##### MSC:
 05C15 Coloring of graphs and hypergraphs
edge colouring
Full Text:
##### References:
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