Computing the metric dimension for chain graphsHenning Fernau, Pinar Heggernes, Pim van 't Hof, Daniel Meister and Reza Saei
Information Processing Letters, vol. 115, pp. 671-676, 2015.
The metric dimension of a graph G is the smallest size of a set R of vertices that can distinguish each vertex pair of G by the shortest-path distance to some vertex in R. Computing the metric dimension is NP-hard, even when restricting inputs to bipartite graphs. We present a linear-time algorithm for computing the metric dimension for chain graphs, which are bipartite graphs whose vertices can be ordered by neighborhood inclusion.