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

Shi Chen; Xuanlong Ma

combinatorics

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

arXiv:2607.27573

summary

The paper proves that any 2‑connected graph that is not a cycle has mixed metric dimension at most twice its cyclomatic number, and uses this bound to settle a conjecture of Sedlar and Åkrekovski.

Abstract

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

11 pages

Topics & keywords

#graph theory #metric dimension #mixed metric dimension #cyclomatic number #2‑connected graphsmixed metric dimensioncyclomatic number2‑connected graphmetric dimensiongraph invariantsconjecture

On the mixed metric dimension of 2-connected graphs

Abstract

Topics & keywords

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