Geodesic
Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 71-93

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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, γt(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, γt2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that γ(G) ≤ γt2(G) ≤ γt(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.
Keywords: domination, semitotal domination, trees 
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     title = {Vertices {Contained} {In} {All} {Or} {In} {No} {Minimum} {Semitotal} {Dominating} {Set} {Of} {A} {Tree}},
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Henning, Michael A.; Marcon, Alister J. Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 71-93. http://geodesic.mathdoc.fr/item/DMGT_2016_36_1_a5/