Trees with equal restrained domination and total restrained domination numbers
Joanna Raczek
Discussiones Mathematicae Graph Theory, Tome 27 (2007), p. 83-91 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:270392 
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Joanna Raczek. Trees with equal restrained domination and total restrained domination numbers. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 83-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1346/

[000] [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. | Zbl 1114.05303

[001] [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.

[002] [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, New York, 1998). | Zbl 0890.05002

[003] [4] M.A. Henning, Trees with equal average domination and independent domination numbers, Ars Combin. 71 (2004) 305-318. | Zbl 1081.05085

[004] [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. | Zbl 1081.05086

[005] [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. | Zbl 0885.68118