## Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S. The total domination number, γt(G), of G is the minimum cardinality of a total dominating set of G. A set S of vertices in G is a disjunctive dominating set in G if every vertex not in S is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it in G. The disjunctive domination number, (Formula presented.) (G), of G is the minimum cardinality of a disjunctive dominating set in G. By definition, we have (Formula presented.) (T)≤γt (T). In this paper, we provide a constructive characterization of the trees T achieving equality in this bound.

Original language | English |
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Pages (from-to) | 531-543 |

Number of pages | 13 |

Journal | Quaestiones Mathematicae |

Volume | 39 |

Issue number | 4 |

DOIs | |

Publication status | Published - 4 Jul 2016 |

## Keywords

- Domination
- disjunctive domination
- trees

## ASJC Scopus subject areas

- Mathematics (miscellaneous)