The metric dimension of a graph G is the size of a smallest subset L ¿ V (G) such that for any x, y ¿ V (G) with x =/ y there is a z ¿ L such that the graph distance between x and z differs from the graph distance between y and z. Even though this notion has been part of the literature for almost 40 years, prior to our work the computational complexity of determining the metric dimension of a graph was still very unclear. In this paper, we show tight complexity boundaries for the Metric Dimen...
Diaz, J., Pottonen, O., Serna, M., van Leeuwen, E.J. Complexity of metric dimension on planar graphs. "Journal of computer and system sciences", 3 Abril 2017, vol. 83, núm. 1, p. 132-158.