## Abstract

Lei G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set, if every vertex not in S is adjacent to a vertex in S and to a vertex in V - S The restrained domination number of G, denoted by γ_{r}(G), is the minimum cardinality of a restrained dominating set of G. A set S ⊆ V is a weak dominating set of G if, for every u in V - S, there exists a v ∈ S such that uv ∈ E and deg u ≥ deg v. The weak domination number of G, denoted by γ_{w}(G) is the minimum cardinality of a weak dominating set of G. In this article we provide a constructive characterization of those trees with equal independent domination and restrained domination numbers. A constructive characterization of those trees with equal independent domination and weak domination numbers is also obtained.

Original language | English |
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Pages (from-to) | 142-153 |

Number of pages | 12 |

Journal | Journal of Graph Theory |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2000 |

Externally published | Yes |

## ASJC Scopus subject areas

- Geometry and Topology