# Trees with equal restrained domination and total restrained domination numbers

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 83-91
- ISSN: 2083-5892

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topJoanna Raczek. "Trees with equal restrained domination and total restrained domination numbers." Discussiones Mathematicae Graph Theory 27.1 (2007): 83-91. <http://eudml.org/doc/270392>.

@article{JoannaRaczek2007,

abstract = {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.},

author = {Joanna Raczek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total restrained domination number; restrained domination number; trees; total restrained set; restrained dominating set},

language = {eng},

number = {1},

pages = {83-91},

title = {Trees with equal restrained domination and total restrained domination numbers},

url = {http://eudml.org/doc/270392},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Joanna Raczek

TI - Trees with equal restrained domination and total restrained domination numbers

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 83

EP - 91

AB - 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.

LA - eng

KW - total restrained domination number; restrained domination number; trees; total restrained set; restrained dominating set

UR - http://eudml.org/doc/270392

ER -

## References

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- [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). Zbl0890.05002
- [4] M.A. Henning, Trees with equal average domination and independent domination numbers, Ars Combin. 71 (2004) 305-318. Zbl1081.05085
- [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. Zbl1081.05086
- [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. Zbl0885.68118

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