## Abstract

A total dominating set of a graph G with no isolated vertex is a set S of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. A paired-dominating set of G is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G is the minimum cardinality of a paired-dominating set of G. Since every paired-dominating set is a total dominating set, the total domination number is bounded above by the paired-domination number. We give a constructive characterization of the trees with equal total domination and paired-domination numbers. Our characterization uses labelings of the vertices that indicates the roles each vertex plays in the sets associated with both parameters.

Original language | English |
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Pages (from-to) | 207-218 |

Number of pages | 12 |

Journal | Utilitas Mathematica |

Volume | 69 |

Publication status | Published - Mar 2006 |

Externally published | Yes |

## Keywords

- Paired-domination
- Total domination
- Trees

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics