## Abstract

A dominating set of a graph G is a subset D ⊆ V_{G} such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γ_{a}(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of V_{G} \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γ_{a}(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.

Original language | English |
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Pages (from-to) | 605-608 |

Number of pages | 4 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

- Accurate domination number
- Corona
- Domination number
- Tree

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics