Complexity and approximation ratio of semitotal domination in graphs

A set S ⊆ V (G) is a semitotal dominating set of a graph G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number γt₂(G) is the minimum cardinality of a semitotal dominating set of G. We show that the semitotal domination problem is APX-complete for bounded-degree graphs, and the semitotal domination problem in any graph of maximum degree ∆ can be approximated with an approximation ratio of 2 +ln(∆− 1).