## Abstract

A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number, γ(G), of G is the cardinality of a minimum 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, γ^{d} _{2}(G), of G is the cardinality of a minimum disjunctive dominating set in G. In this paper, we characterize the vertices contained in all or in no minimum disjunctive dominating set of a tree.

Original language | English |
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Pages (from-to) | 95-123 |

Number of pages | 29 |

Journal | Utilitas Mathematica |

Volume | 105 |

Publication status | Published - Nov 2017 |

## Keywords

- Disjunctive domination
- Domination
- Trees.

## ASJC Scopus subject areas

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