Graphs in the 3-Sphere with Maximum Symmetry

Chao Wang; Shicheng Wang; Yimu Zhang; Bruno Zimmermann

doi:10.1007/s00454-017-9952-1

Graphs in the 3-Sphere with Maximum Symmetry

Chao Wang
, Shicheng Wang^*
, Yimu Zhang
, Bruno Zimmermann

^*Corresponding author for this work

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

4 Scopus citations

Abstract

We consider the orientation-preserving actions of finite groups G on pairs (S³, Γ) , where Γ is a connected graph of genus g> 1 , embedded in S³. For each g we give the maximum order m_g of such G acting on (S³, Γ) for all such Γ ⊂ S³. Indeed we will classify all graphs Γ ⊂ S³ which realize these m_g in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition “orientation-preserving” are also addressed.

Original language	English
Pages (from-to)	331-362
Number of pages	32
Journal	Discrete and Computational Geometry
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s00454-017-9952-1
State	Published - 1 Mar 2018
Externally published	Yes

Keywords

Extendable action
Symmetry of 3-sphere
Symmetry of graph

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10.1007/s00454-017-9952-1

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title = "Graphs in the 3-Sphere with Maximum Symmetry",

abstract = "We consider the orientation-preserving actions of finite groups G on pairs (S3, Γ) , where Γ is a connected graph of genus g> 1 , embedded in S3. For each g we give the maximum order mg of such G acting on (S3, Γ) for all such Γ ⊂ S3. Indeed we will classify all graphs Γ ⊂ S3 which realize these mg in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition “orientation-preserving” are also addressed.",

keywords = "Extendable action, Symmetry of 3-sphere, Symmetry of graph",

author = "Chao Wang and Shicheng Wang and Yimu Zhang and Bruno Zimmermann",

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year = "2018",

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doi = "10.1007/s00454-017-9952-1",

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T1 - Graphs in the 3-Sphere with Maximum Symmetry

AU - Wang, Chao

AU - Wang, Shicheng

AU - Zhang, Yimu

AU - Zimmermann, Bruno

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We consider the orientation-preserving actions of finite groups G on pairs (S3, Γ) , where Γ is a connected graph of genus g> 1 , embedded in S3. For each g we give the maximum order mg of such G acting on (S3, Γ) for all such Γ ⊂ S3. Indeed we will classify all graphs Γ ⊂ S3 which realize these mg in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition “orientation-preserving” are also addressed.

AB - We consider the orientation-preserving actions of finite groups G on pairs (S3, Γ) , where Γ is a connected graph of genus g> 1 , embedded in S3. For each g we give the maximum order mg of such G acting on (S3, Γ) for all such Γ ⊂ S3. Indeed we will classify all graphs Γ ⊂ S3 which realize these mg in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition “orientation-preserving” are also addressed.

KW - Extendable action

KW - Symmetry of 3-sphere

KW - Symmetry of graph

UR - https://www.scopus.com/pages/publications/85038364318

U2 - 10.1007/s00454-017-9952-1

DO - 10.1007/s00454-017-9952-1

M3 - 文章

AN - SCOPUS:85038364318

SN - 0179-5376

VL - 59

SP - 331

EP - 362

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

Graphs in the 3-Sphere with Maximum Symmetry

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Keywords

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