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Two short proofs on total domination. (English) Zbl 1293.05255

Summary: 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 \(\gamma_t(G)\) is the minimum size of a total dominating set. We provide a short proof of the result that \(\gamma_t(G)\leq \frac{2}{3}n\) for connected graphs with \(n\geq 3\) and a short characterization of the extremal graphs.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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