Domination ratio of integer distance digraphs

Jia Huang

doi:10.1016/j.dam.2019.03.001

Domination ratio of integer distance digraphs

Jia Huang

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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)
Pages (from-to)	104-115
Number of pages	12
Journal	Discrete Applied Mathematics
Volume	262
DOIs	https://doi.org/10.1016/j.dam.2019.03.001
State	Published - Jun 15 2019
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2019.03.001

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title = "Domination ratio of integer distance digraphs",

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.",

keywords = "Cayley graph, Circulant graph, Domination ratio, Efficient dominating set, Integer distance graph",

author = "Jia Huang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

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day = "15",

doi = "10.1016/j.dam.2019.03.001",

language = "English (US)",

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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

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VL - 262

SP - 104

EP - 115

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Domination ratio of integer distance digraphs

Abstract

Keywords

ASJC Scopus subject areas

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