## Abstract

We continue the study of {k}-dominating functions in graphs (or integer domination as we shall also say) started by Domke, Hedetniemi, Laskar, and Fricke [5]. For k ≥ 1 an integer, a function f: V(G) → {0, 1,..., k} defined on the vertices of a graph G is called a {k}-dominating function if the sum of its function values over any closed neighborhood is at least k. The weight of a {k}-dominating function is the sum of its function values over all vertices. The {k}-domination number of G is the minimum weight of a {k}-dominating function of G. We study the {k}-domination number on the Cartesian product of graphs, mostly on problems related to the famous Vizing's conjecture. A connection between the {k}-domination number and other domination type parameters is also studied.

Original language | English |
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Pages (from-to) | 1316-1328 |

Number of pages | 13 |

Journal | Taiwanese Journal of Mathematics |

Volume | 10 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

## Keywords

- Cartesian product
- Integer domination
- Vizing's conjecture
- {k}-dominating function

## ASJC Scopus subject areas

- General Mathematics