2 problems

Let $G$ be a graph with no isolated edge. An edge nsd-colouring is an edge colouring $\gamma:E(G)\longrightarrow\\{1,2,\ldots,k\\}$ such that, writing … we have…

Let $G$ be a graph with maximum degree $\Delta$, and let $\chi”_{\sum}(G)$ denote the least number of colours in a proper total colouring whose weighted degrees distinguish adjacen…