## Abstract

The k-restricted total domination number of a graph G is the smallest integer r_{k}(G, γ_{t}) such that given any subset U of k vertices of G, there exists a total dominating set of G of cardinality at most r_{k}(G, γ_{t}) containing U. Hence, the k-restricted total domination number of a graph G measures how many vertices are necessary to totally dominate a graph if an arbitrary set of k vertices must be included in the total dominating set. When k = 0, the k-restricted total domination number is the total domination number. In this paper we establish upper bound on the k-restricted total domination number of a connected graph in terms of the order and the size of the graph.

Original language | English |
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Pages (from-to) | 25-44 |

Number of pages | 20 |

Journal | Discrete Mathematics |

Volume | 289 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 28 Dec 2004 |

Externally published | Yes |

## Keywords

- Bounds
- Restricted total domination number
- Total dominating set

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics