Metric dimension of maximal outerplanar graphs

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if ß(G) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that 2=ß(G)=¿2n5¿ 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 ¿2n5¿ for G. Moreover, we characterize all maximal outerplanar graphs with metric dimension 2.Peer ReviewedPostprint (author's final draft