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## Discussiones Mathematicae Graph Theory

2012 | 32 | 4 | 629-641
Tytuł artykułu

### On the total restrained domination number of direct products of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by $γ_r^t(G)$, is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
629-641
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-04-26
poprawiono
2011-11-28
zaakceptowano
2011-11-30
Twórcy
autor
• Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China
autor
• School of Mathematics and System Sciences, Shandong University Jinan, Shandong Province, 250100, China
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
Bibliografia
• [1] R. Chérifi, S. Gravier, X. Lagraula, C. Payan and I. Zigham, Domination number of cross products of paths, Discrete Appl. Math. 94 (1999) 101-139, doi: 10.1016/S0166-218X(99)00016-5.
• [2] X.G. Chen, W.C. Shiu and H.Y. Chen, Trees with equal total domination and total restrained domination numbers, Discuss. Math. Graph. Theory 28 (2008) 59-66, doi: 10.7151/dmgt.1391.
• [3] M. El-Zahar, S. Gravier and A. Klobucar, On the total domination number of cross products of graphs, Discrete Math. 308 (2008) 2025-2029, doi: 10.1016/j.disc.2007.04.034.
• [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs ( Marcel Dekker, New York, 1998).
• [5] D.X. Ma, X.G. 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] D.F. Rall, Total domination in categorical products of graphs, Discuss. Math. Graph Theory 25 (2005) 35-44, doi: 10.7151/dmgt.1257.
• [7] M. Zwierzchowski, Total domination number of the conjunction of graphs, Discrete Math. 307 (2007) 1016-1020, doi: 10.1016/j.disc.2005.11.047.
Typ dokumentu
Bibliografia
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