Ghalavand–Klavžar–Li local metric dimension bound by clique number

Let $G$ be a graph, with order $n(G)$ and clique number $\omega(G)$. Assume

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

Ghalavand's conjecture. The local metric dimension of $G$ satisfies

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

This conjecture relates the local metric dimension to the clique number. The paper proves the bound for graphs with $\omega(G)\in\{n(G)-1,n(G)-2,n(G)-3\}$; the general case is not resolved here.