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2008 | 28 | 1 | 59-66
Tytuł artykułu

Trees with equal total domination and total restrained domination numbers

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.
Wydawca
Rocznik
Tom
28
Numer
1
Strony
59-66
Opis fizyczny
Daty
wydano
2008
otrzymano
2006-09-22
poprawiono
2007-01-24
zaakceptowano
2007-01-24
Twórcy
  • Department of Mathematics, North China Electric Power University, Beijing 102206, China
  • 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
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1391
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