Geodesic
Total domination versus paired domination
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 435-447

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A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γₜ. The maximal size of an inclusionwise minimal total dominating set, the upper total domination number, is denoted by Γₜ. A paired dominating set is a dominating set whose induced subgraph has a perfect matching. The minimal size of a paired dominating set, the paired domination number, is denoted by γₚ. The maximal size of an inclusionwise minimal paired dominating set, the upper paired domination number, is denoted by Γₚ.
Keywords: total domination, upper total domination, paired domination, upper paired domination, generalized claw-free graphs 
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Schaudt, Oliver. Total domination versus paired domination. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 435-447. http://geodesic.mathdoc.fr/item/DMGT_2012_32_3_a4/