## Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex is adjacent to a vertex in S. The total domination number yγ _{t} (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sd_{γt} (G) of a graph G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the total domination number. Haynes et al. (J. Combin. Math. Combin. Comput. 44 (2003) 115) showed that for any tree T of order at least 3, 1 ≤sd_{γt} (T)≤3. In this paper, we give a constructive characterization of trees whose total domination subdivision number is 3.

Original language | English |
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Pages (from-to) | 195-202 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 286 |

Issue number | 3 |

DOIs | |

Publication status | Published - 28 Sept 2004 |

Externally published | Yes |

## Keywords

- Total domination number
- Total domination subdivision number
- Trees

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics