2 problems

Let $G$ be an undirected graph without twins, and let the location-domination number of $G$ be the minimum cardinality of a dominating set whose vertices have distinct neighborhood…

Let $F_\delta(r,n)$ denote the maximum possible minimum degree among connected $r$-twin-free graphs of order $n$. Auge's conjecture. For every integer $r\geqslant 1$ and every inte…