Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
427105 | Information Processing Letters | 2015 | 6 Pages |
•We show how to compute the metric dimension of bipartite chain graphs.•Our algorithm works in linear time even on compact representations.•We also conclude combinatorial results for simple chain graphs.•Our order-theoretic arguments may be useful for other problems, as well.•We indicate this for some variants of metric dimension.
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.