### Abstract

An integer distance digraph is the Cayley graph Γ(Z,S) of the additive group Z of all integers with respect to some finite subset S⊆Z. The domination ratio of Γ(Z,S) is the minimum density of a dominating set in Γ(Z,S). We establish some basic results on the domination ratio of Γ(Z,S) and precisely determine it when S={s,t} with s dividing t.

Original language | English (US) |
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Pages (from-to) | 104-115 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 262 |

DOIs | |

Publication status | Published - Jun 15 2019 |

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### Keywords

- Cayley graph
- Circulant graph
- Domination ratio
- Efficient dominating set
- Integer distance graph

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics