## Abstract

For a positive integer k, a k-subdominating function of a graph G=(V,E) is a function f: V→{-1,1} such that ∑u∈N _{G}[v]f(u)1 for at least k vertices v of G. The k-subdomination number of G, denoted by γ _{ks}(G), is the minimum of ∑ _{v∈V}f(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed by Cockayne and Mynhardt. We also give a lower bound for γ _{ks}(G) in terms of the degree sequence of G. This generalizes some known results on the k-subdomination number γ _{ks}(G), the signed domination number γ _{s}(G) and the majority domination number γ _{maj}(G).

Original language | English |
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Pages (from-to) | 55-60 |

Number of pages | 6 |

Journal | Discrete Applied Mathematics |

Volume | 120 |

Issue number | 1-3 |

DOIs | |

State | Published - 15 Aug 2002 |

## Keywords

- Domination
- k-subdomination
- Leaf
- Majority domination
- Signed domination
- Tree