6 problems

Let $G$ be a finite graph. A set $C\subseteq V(G)$ is a locating-dominating set if it dominates every vertex outside $C$ and, for every two distinct vertices…

Location-domination conjecture. If $G$ is a twin-free graph on $n$ vertices, then

Two-thirds conjecture. Every twin-free isolate-free graph $G$ of order $n$ satisfies

Let $K$ denote the infinite king grid, and let $\operatorname{DET:LD}(K)$ denote its deterministic locating-dominating density. Deterministic locating-dominating density conjecture…

Let $G$ be a graph of order $n$ with no isolated vertices. A graph is twin-free if no two distinct vertices have the same open or closed neighborhood, and let $\gamma_L(G)$ be its…

Let $\lambda_{|\mathcal C^*}(n)$ denote the maximum location-domination number of a twin-free, connected graph on $n$ vertices. Garijo–González–Márquez conjecture. There exists a p…