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For a graph G = (V; E), a set S V (G) is a total dominating set if it is dominating and both hSi has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S V (G) is a total restrained dominating set if it is total dominating and hV (G) Si has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.

Trees with equal total and total restrained domination numbers