## Abstract

The relationship ρ_{L} (G) ≤ ρ (G) ≤ γ (G) between the lower packing number ρ_{L} (G), the packing number ρ (G) and the domination number γ (G) of a graph G is well known. In this paper we establish best possible bounds on the ratios of the packing numbers of any (connected) graph to its six domination-related parameters (the lower and upper irredundance numbers i r and I R, the lower and upper independence numbers i and β, and the lower and upper domination numbers γ and Γ). In particular, best possible constants a_{θ}, b_{θ}, c_{θ} and d_{θ} are found for which the inequalities a_{θ} θ (G) ≤ ρ_{L} (G) ≤ b_{θ} θ (G) and c_{θ} θ (G) ≤ ρ (G) ≤ d_{θ} θ (G) hold for any connected graph G and all θ ∈ {i r, γ, i, β, Γ, I R}. From our work it follows, for example, that ρ_{L} (G) ≤ frac(3, 2) i r (G) and ρ (G) ≤ frac(3, 2) i r (G) for any connected graph G, and that these inequalities are best possible.

Original language | English |
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Pages (from-to) | 2473-2478 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 8 |

DOIs | |

Publication status | Published - 28 Apr 2009 |

Externally published | Yes |

## Keywords

- Domination
- Graph packing
- Graph parameter ratios
- Independence
- Irredundance

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics