Vertices contained in all or in no minimum semitotal dominating set of a tree

Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important dom- ination parameters; namely, the domination number, (G), and the total domination number, Υ(G). A set S of vertices in a graph G 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, Υ2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that (G) ≤ Υ2(G) ≤ Υ(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.