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2006 | 26 | 1 | 103-112
Tytuł artykułu

Some results on total domination in direct products of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
Wydawca
Rocznik
Tom
26
Numer
1
Strony
103-112
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-02-09
poprawiono
2005-07-15
Twórcy
autor
  • UJF, ERTé Maths à Modeler, GéoD research group, Leibniz laboratory, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France
  • CNRS, ERTé Maths à Modeler, GéoD research group, Leibniz laboratory, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France
  • Department of Mathematics and Computer Science, PeF, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia
  • University of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia
Bibliografia
  • [1] B. Bresar, S. Klavžar and D.F. Rall, Dominating direct products of graphs, submitted, 2004.
  • [2] M. El-Zahar, S. Gravier and A. Klobucar, On the total domination of cross products of graphs, Les Cahiers du laboratoire Leibniz, No. 97, January 2004.
  • [3] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213.
  • [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Fundamentals of Domination in Graphs (Marcel Dekker, Inc. New York, 1998).
  • [5] W. Imrich, Factoring cardinal product graphs in polynomial time, Discrete Math. 192 (1998) 119-144, doi: 10.1016/S0012-365X(98)00069-7.
  • [6] W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition (J. Wiley & Sons, New York, 2000).
  • [7] P.K. Jha, S. Klavžar and B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs, Discuss. Math. Graph Theory 17 (1997) 301-309, doi: 10.7151/dmgt.1057.
  • [8] R. Klasing and C. Laforest, Hardness results and approximation algorithms of k-tuple domination in graphs, Inform. Process. Lett. 89 (2004) 75-83, doi: 10.1016/j.ipl.2003.10.004.
  • [9] C.S. Liao and G.J. Chang, Algorithmic aspect of k-tuple domination in graphs, Taiwanese J. Math. 6 (2002) 415-420.
  • [10] R. Nowakowski and D. F. Rall, Associative graph products and their independence, domination and coloring numbers, Discuss. Math. Graph Theory 16 (1996) 53-79, doi: 10.7151/dmgt.1023.
  • [11] D.F. Rall, Total domination in categorical products of graphs, Discuss. Math. Graph Theory 25 (2005) 35-44, doi: 10.7151/dmgt.1257.
  • [12] P.M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc. 13 (1962) 47-52, doi: 10.1090/S0002-9939-1962-0133816-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1305
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