Ghalavand et al.'s local metric dimension bound by clique number

Let $G$ be a graph with order $n(G)$, clique number $(G)$, and local metric dimension $_l(G)$. Assume

$$n(G)\geq (G)+1\geq 4.$$

Ghalavand et al.'s conjecture.

$$\dim_l(G)\leq\left\lfloor \left(\frac{(G) - 2}{(G) - 1}\right)n(G)\right\rfloor.$$

The conjecture was posed as Conjecture 2 in the cited earlier work and is confirmed by the present paper, so it is now a theorem.