On the mixed metric dimension of $2$-connected graphs

Abstract

We show that for a $2$-connected graph $G$ which is not a cycle, the mixed metric dimension of $G$ is at most $2c(G)$, where $c(G)$ is the cyclomatic number of $G$. As an immediate application, we prove a conjecture proposed by Sedlar and \v{S}krekovski (2021).