The mixed metric dimension bound for graphs

Let $G\ne C_n$ be a graph, and let $c(G)$ denote its cyclomatic number. The quantity $L_1(G)$ is the parameter used in the mixed metric dimension bound, and $\mathrm{mdim}(G)$ denotes the mixed metric dimension of $G$. Mixed metric dimension conjecture.

$$\mathrm{mdim}(G)\leq L_1(G)+2c(G).$$

The bound is established in the paper for cactus graphs, including trees and unicyclic graphs, where the number of edge-disjoint cycles equals the cyclomatic number. The conjecture asks whether the same inequality holds for general graphs; the supplied source gives no resolution.