The vertex metric dimension bound for connected graphs

Let $G$ be a connected graph. The invariant $L(G)$ is the graph parameter measuring the contribution of leaves, and $c(G)$ is the cyclomatic number of $G$. The vertex metric dimension bound conjecture.

$$\mathrm{dim}(G)\leq L(G)+2c(G).$$

This extends the corresponding bound known for cactus graphs to all connected graphs. The source gives no resolution of the conjecture.