The location-domination conjecture for twin-free graphs

Let $G$ be a graph on $n$ vertices. A twin-free graph is one with no two distinct vertices having the same open neighborhood, and $LD(G)$ denotes its location-domination number.

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

$$LD(G)\leq \frac{n}{2}.$$

This conjecture, due to Garijo, González and Márquez, concerns the size of a smallest locating-dominating set in a twin-free graph. The source proves the weaker bound $LD(G)\leq \lceil\frac{5}{8}n\rceil$, improving the earlier bound $\lfloor\frac{2}{3}n\rfloor$, so the conjectured bound remains open in the supplied source.