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 t 2)( G ), is the minimum cardinality of a semitotal dominating set of G . We observe that γ( G ) ≤ _(γ t 2)( 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.
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