Garijo et al.'s locating-dominating set conjecture for twin-free graphs

Let $G$ be a twin-free graph of order $n$ without isolated vertices. A locating-dominating set is a dominating set $D$ such that every two distinct vertices outside $D$ have distinct neighborhoods in $D$; let $\gamma_L(G)$ denote the minimum cardinality of a locating-dominating set of $G$.

Garijo et al.'s conjecture. Every twin-free graph $G$ of order $n$ without isolated vertices satisfies

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

This conjecture proposes a universal upper bound on the locating-dominating number of twin-free graphs. The supplied source does not indicate whether the conjecture has been resolved.