The Outer-Paired Domination of Graphs

In this paper, we introduce a new variant of domination called the outer-paired domination. For a graph G = (V, E), an outer-paired dominating set D subset of V is a dominating set of G such that the induced subgraph of V\D contains a perfect matching. The outer-paired domination number of a graph G is the cardinality of a minimum outer-paired dominating set of G. We show that finding the outer-paired domination number of a graph G is NP-hard on bipartite graphs, chordal graphs, and planar graphs. We also propose a linear-time algorithm for solving the outer-paired domination problem on trees.