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 
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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[1] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar and L.R. Marcus, Restrained domination in graphs, Discrete Math. 203 (1999) 61-69, doi: 10.1016/S0012-365X(99)00016-3.

[2] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi and L.R. Marcus, Restrained domination in trees, Discrete Math. 211 (2000) 1-9, doi: 10.1016/S0012-365X(99)00036-9.

[3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, New York, 1998).

[4] M.A. Henning, Trees with equal average domination and independent domination numbers, Ars Combin. 71 (2004) 305-318.

[5] D. Ma, X. Chen and L. Sun, On total restrained domination in graphs, Czechoslovak Math. J. 55 (2005) 165-173, doi: 10.1007/s10587-005-0012-2.

[6] J.A. Telle and A. Proskurowski, Algorithms for vertex partitioning problems on partial k-trees, SIAM J. Discrete Math. 10 (1997) 529-550, doi: 10.1137/S0895480194275825.