Opuscula Math. 24, no. 2 (2004), 223-229

Opuscula Mathematica

# A note on the vertex-distinguishing index for some cubic graphs

Karolina Taczuk
Mariusz Woźniak

Abstract. The vertex-distinguishing index of a graph $$G$$ ($$\operatorname{vdi}(G)$$) is the minimum number of colours required to colour properly the edges of a graph in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some families of cubic graphs.

Keywords: edge colouring, vertex-distinguishing colouring, cubic graphs.

Mathematics Subject Classification: 05C15.

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• Karolina Taczuk
• School of Economics and Computer Science, ul. Św. Filipa 17, 31-150 Cracow, Poland
• Mariusz Woźniak
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland