### 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 | |

State | Published - Jun 15 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

**Domination ratio of integer distance digraphs.** / Huang, Jia.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 262, pp. 104-115. https://doi.org/10.1016/j.dam.2019.03.001

}

TY - JOUR

T1 - Domination ratio of integer distance digraphs

AU - Huang, Jia

PY - 2019/6/15

Y1 - 2019/6/15

N2 - 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.

AB - 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.

KW - Cayley graph

KW - Circulant graph

KW - Domination ratio

KW - Efficient dominating set

KW - Integer distance graph

UR - http://www.scopus.com/inward/record.url?scp=85063029466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063029466&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2019.03.001

DO - 10.1016/j.dam.2019.03.001

M3 - Article

AN - SCOPUS:85063029466

VL - 262

SP - 104

EP - 115

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -