SEMITOTAL DOMINATION IN CLAW-FREE GRAPHS

In an isolate-free graph G, a subset S of vertices is a semitotal dominating set of 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 of G, denoted by 7t2(G), is the minimum cardinality of a semitotal dominating set in G. We prove that if G is a connected claw-free graph of order n with minimum degree delta(G) ,, 2 and is not one of fourteen exceptional graphs (ten of which are cycles), then 7t2(G) 5 37 n, and we also characterize the graphs achieving equality, which are an infinite family of graphs. In particular, if we restrict (2014) 67-81].