3 problems

Let $\overleftrightarrow{K_n}$ be the complete symmetric digraph on $n$ vertices. Write $\chi'_{D_{2}}(\overleftrightarrow{K_n})$ for its distinguishing proper arc-colouring number…

Ferrara–Flesch–Gethner's conjecture. For every finite graph $G$,

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.…