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ArticleOriginal scientific text

Title

Some results on total domination in direct products of graphs

Authors 1, 2, 3, 4

Affiliations

  1. UJF, ERTé Maths à Modeler, GéoD research group, Leibniz laboratory, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France
  2. CNRS, ERTé Maths à Modeler, GéoD research group, Leibniz laboratory, 46 av. Félix Viallet, 38031 Grenoble CEDEX, France
  3. Department of Mathematics and Computer Science, PeF, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia
  4. University of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia

Abstract

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.

Keywords

ENG
direct product, total domination, k-tuple domination, open packing, domination

Bibliography

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Discussiones Mathematicae Graph Theory
2006/26/1
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Pages:
103-112
Main language of publication
English
Received
2005-02-09
Accepted
2005-07-15
Published
2006

DOI: 10.7151/dmgt.1305

Exact and natural sciences