Vertices contained in all or in no minimum semitotal dominating set of a tree
Michael A. Henning, Alister J. Marcon · Discussiones Mathematicae Graph Theory · 2015
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 domination parameters; namely, the domination number, γ(G), and the total domination number, γ t (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, γ t2 (G), is the minimum cardinality of a semitotal dominating set of G.We observe that γ(G) ≤ γ t2 (G) ≤ γ t (G).We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.