Geodesic
Two Short Proofs on Total Domination
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 457-459

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A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph γt (G) is the minimum size of a total dominating set. We provide a short proof of the result that γt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.
Keywords: total domination 
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Bickle, Allan. Two Short Proofs on Total Domination. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 457-459. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a16/