Geodesic
Trees with equal restrained domination and total restrained domination numbers
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 83-91.

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For a graph G = (V,E), a set D ⊆ V(G) is a total restrained dominating set if it is a dominating set and both 〈D〉 and 〈V(G)-D〉 do not have isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. A set D ⊆ V(G) is a restrained dominating set if it is a dominating set and 〈V(G)-D〉 does not contain an isolated vertex. The cardinality of a minimum restrained dominating set in G is the restrained domination number. We characterize all trees for which total restrained and restrained domination numbers are equal.
Keywords: total restrained domination number, restrained domination number, trees 
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Raczek, Joanna. Trees with equal restrained domination and total restrained domination numbers. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 83-91. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a7/

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