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Let G = (V, E) be a graph. A set D ⊆ V is a total outer-connected dominating set of G if D is dominating and G[V - D] is connected. The total outer-connected domination number of G, denoted γtc(G), is the smallest cardinality of a total outer-connected dominating set of G. It is known that if T is a tree of order n ≥ 2, then 
. We will provide a constructive characterization for trees achieving the latter bound.
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