## Abstract

For a vertex D of a graph G = (V,E), the domination number γ_{v}(G) of G relative to v is the minimum cardinality of a dominating set in G that contains v. The average domination number of G is γ_{av}(G) = 1/|V| ∑_{v∈V}(G). The independent domination number i_{v}(G) of G relative to v is the minimum cardinality of a maximal independent set in G that contains v. The average independent domination number of G is i_{av}(G) = 1/|V| ∑_{v∈V} i_{v}(G). In this paper, we show that a tree T satisfies γ_{av}(T) = i_{av}(T) if and only if A(T) = Φ or each vertex of A(T) has degree 2 in T, where A(T) is the set of vertices of T that are contained in all its minimum dominating sets.

Original language | English |
---|---|

Pages (from-to) | 305-318 |

Number of pages | 14 |

Journal | Ars Combinatoria |

Volume | 71 |

Publication status | Published - Apr 2004 |

Externally published | Yes |

## Keywords

- Average domination
- Average independent domination
- Trees

## ASJC Scopus subject areas

- General Mathematics