A characterization of trees with unique minimum double dominating sets - Chellali, Mustapha; Haynes, Teresa W. (Utilitas Mathematica, 2010)
In a graph G = (V, E), a vertex dominates itself and its neighbors. A subset S of vertices of V is a double dominating set if every vertex of V is dominated at least twice by the vertices of S. We give a constructive characterization of trees with unique minimum double dominating sets.