## Abstract

Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γ_{k} (G), the connected k-domination number γ_{k}^{c} (G); the k-independent domination number γ_{k}^{i} (G) and the k-irredundance number ir_{k} (G). The authors prove that if an ir_{k}-set X is a k-independent set of G, then ir_{k} (G) = γ_{k} (G) = γ_{k}^{i} (G), and that for k ≥ 2, γ_{k}^{c} (G) = 1 if ir_{k} (G) = 1, γ_{k}^{c} (G) ≤ max { (2 k + 1) ir_{k} (G) - 2 k, frac(5, 2) ir_{k} (G) k - frac(7, 2) k + 2 } if ir_{k} (G) is odd, and γ_{k}^{c} (G) ≤ frac(5, 2) ir_{k} (G) k - 3 k + 2 if ir_{k} (G) is even, which generalize some known results.

Original language | English (US) |
---|---|

Pages (from-to) | 2943-2953 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 306 |

Issue number | 22 |

DOIs | |

State | Published - Nov 28 2006 |

Externally published | Yes |

## Keywords

- Connected k-domination number
- k-Domination number
- k-Independent domination number
- k-Independent set
- k-Irredundance number

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics