Geodesic
Trees with equal restrained domination and total restrained domination numbers
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 83-91 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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 
@article{DMGT_2007_27_1_a7,
     author = {Raczek, Joanna},
     title = {Trees with equal restrained domination and total restrained domination numbers},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {83--91},
     year = {2007},
     volume = {27},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a7/}
}
TY  - JOUR
AU  - Raczek, Joanna
TI  - Trees with equal restrained domination and total restrained domination numbers
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 83
EP  - 91
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a7/
LA  - en
ID  - DMGT_2007_27_1_a7
ER  - 
%0 Journal Article
%A Raczek, Joanna
%T Trees with equal restrained domination and total restrained domination numbers
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 83-91
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a7/
%G en
%F DMGT_2007_27_1_a7
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/

[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.