$k$-Tuple Total Domination in Supergeneralized Petersen Graphs

Authors

  • Adel P. Kazemi Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili
  • Behnaz Pahlavsay Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili

DOI:

https://doi.org/10.26713/cma.v2i1.130

Keywords:

$k$-tuple total domination number, Supergeneralized Petersen graph, Cartesian product graph

Abstract

Total domination number of a graph without isolated vertex is the minimum cardinality of a total dominating set, that is, a set of vertices such that every vertex of the graph is adjacent to at least one vertex of the set. Henning and Kazemi in [4] extended this definition as follows: for any positive integer $k$, and any graph $G$ with minimum degree-$k$, a set $D $ of vertices is a $k$-tuple total dominating set of $G$ if each vertex of $G$ is adjacent to at least $k$ vertices in $D$. The $k$-tuple total domination number $\gamma _{\times k,t}(G)$ of $G$ is the minimum cardinality of a $k$-tuple total dominating set of $G$. In this paper, we give some upper bounds for the $k$-tuple total domination number of the supergeneralized Petersen graphs. Also we calculate the exact amount of this number for some of them.

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CITATION

How to Cite

Kazemi, A. P., & Pahlavsay, B. (2011). $k$-Tuple Total Domination in Supergeneralized Petersen Graphs. Communications in Mathematics and Applications, 2(1), 29–38. https://doi.org/10.26713/cma.v2i1.130

Issue

Vol. 2 No. 1 (2011)

Section

Research Article

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