The Outer-Paired Domination of Graphs

Abstract

In this paper, we introduce a new variant of domination called the outer-paired domination. For a graph [Formula: see text], an outer-paired dominating set [Formula: see text] is a dominating set of [Formula: see text] such that the induced subgraph of [Formula: see text] contains a perfect matching. The outer-paired domination number of a graph [Formula: see text] is the cardinality of a minimum outer-paired dominating set of [Formula: see text]. We show that finding the outer-paired domination number of a graph [Formula: see text] 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.