Graphs in the 3-Sphere with Maximum Symmetry
We consider the orientation-preserving actions of finite groups G on pairs ( S 3 , Γ ) , where Γ is a connected graph of genus g > 1 , embedded in S 3 . For each g we give the maximum order m g of such G acting on ( S 3 , Γ ) for all such Γ ⊂ S 3 . Indeed we will classify all graphs Γ ⊂ S 3 which...
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| Veröffentlicht in: | Discrete & computational geometry 2018-03, Vol.59 (2), p.331-362 |
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| container_title | Discrete & computational geometry |
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| creator | Wang, Chao Wang, Shicheng Zhang, Yimu Zimmermann, Bruno |
| description | We consider the orientation-preserving actions of finite groups
G
on pairs
(
S
3
,
Γ
)
, where
Γ
is a connected graph of genus
g
>
1
, embedded in
S
3
. For each
g
we give the maximum order
m
g
of such
G
acting on
(
S
3
,
Γ
)
for all such
Γ
⊂
S
3
. Indeed we will classify all graphs
Γ
⊂
S
3
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. |
| doi_str_mv | 10.1007/s00454-017-9952-1 |
| format | Article |
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G
on pairs
(
S
3
,
Γ
)
, where
Γ
is a connected graph of genus
g
>
1
, embedded in
S
3
. For each
g
we give the maximum order
m
g
of such
G
acting on
(
S
3
,
Γ
)
for all such
Γ
⊂
S
3
. Indeed we will classify all graphs
Γ
⊂
S
3
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.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-017-9952-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computational Mathematics and Numerical Analysis ; Graphs ; Mathematics ; Mathematics and Statistics</subject><ispartof>Discrete & computational geometry, 2018-03, Vol.59 (2), p.331-362</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Discrete & Computational Geometry is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-3ce0643206dceea60f9a46b74533e8fb878096d5a3fd70b3d8c287328a436f6b3</citedby><cites>FETCH-LOGICAL-c359t-3ce0643206dceea60f9a46b74533e8fb878096d5a3fd70b3d8c287328a436f6b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00454-017-9952-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-017-9952-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Wang, Chao</creatorcontrib><creatorcontrib>Wang, Shicheng</creatorcontrib><creatorcontrib>Zhang, Yimu</creatorcontrib><creatorcontrib>Zimmermann, Bruno</creatorcontrib><title>Graphs in the 3-Sphere with Maximum Symmetry</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>We consider the orientation-preserving actions of finite groups
G
on pairs
(
S
3
,
Γ
)
, where
Γ
is a connected graph of genus
g
>
1
, embedded in
S
3
. For each
g
we give the maximum order
m
g
of such
G
acting on
(
S
3
,
Γ
)
for all such
Γ
⊂
S
3
. Indeed we will classify all graphs
Γ
⊂
S
3
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.</description><subject>Combinatorics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Graphs</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0179-5376</issn><issn>1432-0444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kD9PwzAUxC0EEqXwAdgisWJ4zvPfEVVQkIoYCrPlJA5JRdpgJ4J-e1yFgYXpDfe7O70j5JLBDQNQtxGAC06BKWqMyCk7IjPGMafAOT8msyQYKlDJU3IW4wYSbkDPyPUyuL6JWbvNhsZnSNd944PPvtqhyZ7dd9uNXbbed50fwv6cnNTuI_qL3zsnbw_3r4tHunpZPi3uVrREYQaKpQeZukFWpfdOQm0cl4XiAtHrutBKg5GVcFhXCgqsdJlrhbl2HGUtC5yTqym3D7vP0cfBbnZj2KZKy4zSIlcGRaLYRJVhF2Pwte1D27mwtwzsYRQ7jWLT7_YwimXJk0-emNjtuw9_kv81_QAqcmIz</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Wang, Chao</creator><creator>Wang, Shicheng</creator><creator>Zhang, Yimu</creator><creator>Zimmermann, Bruno</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20180301</creationdate><title>Graphs in the 3-Sphere with Maximum Symmetry</title><author>Wang, Chao ; Wang, Shicheng ; Zhang, Yimu ; Zimmermann, Bruno</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-3ce0643206dceea60f9a46b74533e8fb878096d5a3fd70b3d8c287328a436f6b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Chao</creatorcontrib><creatorcontrib>Wang, Shicheng</creatorcontrib><creatorcontrib>Zhang, Yimu</creatorcontrib><creatorcontrib>Zimmermann, Bruno</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Discrete & computational geometry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Chao</au><au>Wang, Shicheng</au><au>Zhang, Yimu</au><au>Zimmermann, Bruno</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Graphs in the 3-Sphere with Maximum Symmetry</atitle><jtitle>Discrete & computational geometry</jtitle><stitle>Discrete Comput Geom</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>59</volume><issue>2</issue><spage>331</spage><epage>362</epage><pages>331-362</pages><issn>0179-5376</issn><eissn>1432-0444</eissn><abstract>We consider the orientation-preserving actions of finite groups
G
on pairs
(
S
3
,
Γ
)
, where
Γ
is a connected graph of genus
g
>
1
, embedded in
S
3
. For each
g
we give the maximum order
m
g
of such
G
acting on
(
S
3
,
Γ
)
for all such
Γ
⊂
S
3
. Indeed we will classify all graphs
Γ
⊂
S
3
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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00454-017-9952-1</doi><tpages>32</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Discrete & computational geometry, 2018-03, Vol.59 (2), p.331-362 |
| issn | 0179-5376 1432-0444 |
| language | eng |
| recordid | cdi_proquest_journals_1978527935 |
| source | SpringerNature Journals |
| subjects | Combinatorics Computational Mathematics and Numerical Analysis Graphs Mathematics Mathematics and Statistics |
| title | Graphs in the 3-Sphere with Maximum Symmetry |
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