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Let t(G) and 2(G) be the total domination number and the 2domination number of a graph G, respectively. It has been shown that: t(T ) 2(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.

A characterization of (γt,γ2)-trees

A characterization of (γ_t,γ₂)-trees