# Metric dimension of maximal outerplanar graphs

## TL;DR

This paper investigates the metric dimension of maximal outerplanar graphs, establishing tight bounds, characterizing graphs with metric dimension 2, and providing linear algorithms for related decision and construction problems.

## Contribution

It proves tight bounds for the metric dimension of maximal outerplanar graphs and offers linear algorithms for key decision and construction tasks.

## Key findings

- Bounds for metric dimension: 2 to ⌈2n/5⌉, tight bounds.
- Linear algorithms for deciding metric dimension 2.
- Characterization of graphs with metric dimension 2.

## Abstract

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if $\beta (G)$ is the metric dimension of a maximal outerplanar graph $G$ of order $n$, we prove that $2\le \beta (G) \le \lceil \frac{2n}{5}\rceil$ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of $G$ is 2 and to build a resolving set of size $\lceil \frac{2n}{5}\rceil$ for $G$. Moreover, we characterize the maximal outerplanar graphs with metric dimension 2.