4 problems

Distant total sum distinguishing conjecture. For every positive integer $r$ there exists a constant $C$ such that

Let $G=(V,E)$ be a graph, and let $c:V\cup E\to\{1,2,\ldots,k\}$ be a proper total colouring. For each vertex $v$, define its total sum by … Let $\chi”_{\Sigma}(G)$ be the least…

Let $G$ be a graph, let $Delta(G)$ and $delta(G)$ denote its maximum and minimum degrees, and let $chi”_{a,r}(G)$ denote its $r$-distant set distinguishing total chromatic number.…

The 1-2 Conjecture. Every graph has a total $2$-weighting whose resulting vertex sums form a proper colouring; equivalently,