On the total neighbour sum distinguishing index of graphs with bounded maximum average degree

Hervé Hocquard, Jakub Przybyło

A proper total $k$-colouring of a graph $G=(V,E)$ is an assignment $c:V\cup E\to \{1,2,\dots ,k\}$ of colours to the edges and the vertices of $G$ such that no two adjacent edge…