Geodesic
A characterization of (γₜ,γ₂)-trees
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 425-435

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Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.
Keywords: domination, total domination, 2-domination, (λ,μ)-tree 
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Lu, You; Hou, Xinmin; Xu, Jun-Ming; Li, Ning. A characterization of (γₜ,γ₂)-trees. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 425-435. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a5/