## 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.)

total domination
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