On the neighbour sum distinguishing index of planar graphs

Marthe Bonamy, Jakub Przybyło

Let $c$ be a proper edge colouring of a graph $G=(V,E)$ with integers $1,2,\dots ,k$. Then $k\ge \Delta (G)$, while by Vizing's theorem, no more than $k=\Delta (G)+1$ is necessary for constru…