## Abstract

A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number ^{γt}(G) is the minimum cardinality of a total dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we investigate relationships between the annihilation number and the total domination number of a graph. Let T be a tree of order n<2. We show that ^{γt}(T)≤a(T)+1, and we characterize the extremal trees achieving equality in this bound.

Original language | English |
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Pages (from-to) | 349-354 |

Number of pages | 6 |

Journal | Discrete Applied Mathematics |

Volume | 161 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 2013 |

## Keywords

- Annihilation number
- Total domination
- Total domination number

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics