A linear time algorithm for computing a minimum paired-dominating set of a convex bipartite graph

A set D of vertices of a graph G = (V, E) is a dominating set of G if every vertex in V\D has at least one neighbor in D.A dominating set D of G is a paired-dominating set of G if the induced subgraph, G[D], has a perfect matching. The paired-domination problem is for a given graph G and a positive integer k to answer if G has a paired-dominating set of size at most k. The paired-domination problem is known to be NP-complete even for bipartite graphs. In this paper, we propose a linear time algorithm to compute a minimum paired-dominating set of a convex bipartite graph. (c) 2012 Elsevier B.V. All rights reserved.