NP-completeness and APX-completeness of restrained domination in graphs

Let G=(V,E) be a simple graph. A vertex set S⊆V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V−S. In this paper, we investigate the NP-completeness of the restrained domination problem in planar graphs and split graphs. Meanwhile, it is proved that the restrained domination problem is APX-complete for bounded-degree graphs.