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## Discussiones Mathematicae Graph Theory

2008 | 28 | 1 | 59-66
Tytuł artykułu

### Trees with equal total domination and total restrained domination numbers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V(G) is a total restrained dominating set if it is total dominating and ⟨V(G)-S⟩ has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
59-66
Opis fizyczny
Daty
wydano
2008
otrzymano
2006-09-22
poprawiono
2007-01-24
zaakceptowano
2007-01-24
Twórcy
autor
• Department of Mathematics, North China Electric Power University, Beijing 102206, China
autor
• Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China
autor
• The College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong Province 266510, China
Bibliografia
• [1] S. Arumugam and J. Paulraj Joseph, On graphs with equal domination and connected domination numbers, Discrete Math. 206 (1999) 45-49, doi: 10.1016/S0012-365X(98)00390-2.
• [2] 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.
• [3] F. Harary and M. Livingston, Characterization of tree with equal domination and independent domination numbers, Congr. Numer. 55 (1986) 121-150.
• [4] 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.
• [5] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi and L.R. Markus, Restrained domination in trees, Discrete Math. 211 (2000) 1-9, doi: 10.1016/S0012-365X(99)00036-9.
• [6] E.J. Cockayne, C.M. Mynhardt and B. Yu, Total dominating functions in trees: minimality and convexity, J. Graph Theory 19 (1995) 83-92, doi: 10.1002/jgt.3190190109.
Typ dokumentu
Bibliografia
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