In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if \(\beta (G)\) denotes 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 S of size \(\lceil \frac{2n}{5}\rceil \) for G. Moreover, we characterize all maximal outerplanar graphs with metric dimension 2.

中文翻译：

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最大外平面图的度量维

在本文中，我们研究了最大外平面图中的度量维数问题。具体来说，如果\（\ beta（G）\）表示阶次为n的最大外平面图G的度量尺寸，我们证明\（2 \ le \ beta（G）\ le \ lceil \ frac {2n} {5 } \ rceil \）的边界是紧密的。我们还提供了线性算法来决定的度量尺寸是否ģ是2，并建立一个解决组小号尺寸的\（\ lceil \压裂{2N} {5} \ rceil \）为G ^。此外，我们用度量维2来刻画所有最大的外平面图。