Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices
We show that, up to isomorphism, there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2 n for each even number n ≥ 4. This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs ( Discrete Math. , 256 , 301–334 (2002)). As a...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2023-04, Vol.39 (4), p.618-632 |
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| creator | Kovács, István |
| description | We show that, up to isomorphism, there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2
n
for each even number
n
≥ 4. This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs (
Discrete Math.
,
256
, 301–334 (2002)). As an application, a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups, which generalises the earlier formula of Huang et al. dealing with the particular case when
n
is a prime (
Acta Math. Sin., Engl. Ser.
,
33
, 996–1011 (2017)). As another application, a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve (arXiv preprint, (2007)). |
| doi_str_mv | 10.1007/s10114-023-1415-4 |
| format | Article |
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n
for each even number
n
≥ 4. This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs (
Discrete Math.
,
256
, 301–334 (2002)). As an application, a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups, which generalises the earlier formula of Huang et al. dealing with the particular case when
n
is a prime (
Acta Math. Sin., Engl. Ser.
,
33
, 996–1011 (2017)). As another application, a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve (arXiv preprint, (2007)).</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-023-1415-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Graphs ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Matrices ; Matrix</subject><ispartof>Acta mathematica Sinica. English series, 2023-04, Vol.39 (4), p.618-632</ispartof><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023</rights><rights>Springer-Verlag GmbH Germany & The Editorial Office of AMS 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-da007418faff54cccfdf2012fe110a78afb3d56a85afeb89a1c4edc9a86cb2083</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/s10114-023-1415-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-023-1415-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Kovács, István</creatorcontrib><title>Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><description>We show that, up to isomorphism, there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2
n
for each even number
n
≥ 4. This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs (
Discrete Math.
,
256
, 301–334 (2002)). As an application, a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups, which generalises the earlier formula of Huang et al. dealing with the particular case when
n
is a prime (
Acta Math. Sin., Engl. Ser.
,
33
, 996–1011 (2017)). As another application, a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve (arXiv preprint, (2007)).</description><subject>Graphs</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrices</subject><subject>Matrix</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kDFPwzAQhS0EEqXwA9gsMQd8iZ04IwpQkIoYKLN1cWyaKo2DnQz997hKJSamOz299-70EXIL7B4YKx4CMACesDRLgINI-BlZAM_KpMihOD_tUkB-Sa5C2DEmRMnyBdm8Bbd3fti2YR-os7Sa6lbTCg-dOdCVx2Eb5Z4-tVvTeOyi5KYhUOwb-jmgD4ZWrddTh_1I33H0rTbhmlxY7IK5Oc0l-Xp53lSvyfpj9VY9rhOd5nJMGoyfc5AWrRVca20bmzJIrQFgWEi0ddaIHKVAa2pZImhuGl2izHWdMpktyd3cO3j3M5kwqp2bfB9PqlRCxiIScXTB7NLeheCNVYNv9-gPCpg6wlMzPBXhqSM8xWMmnTMhevtv4_-a_w_9Alsnco0</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Kovács, István</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20230401</creationdate><title>Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices</title><author>Kovács, István</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-da007418faff54cccfdf2012fe110a78afb3d56a85afeb89a1c4edc9a86cb2083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Graphs</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrices</topic><topic>Matrix</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kovács, István</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kovács, István</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>39</volume><issue>4</issue><spage>618</spage><epage>632</epage><pages>618-632</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>We show that, up to isomorphism, there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2
n
for each even number
n
≥ 4. This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs (
Discrete Math.
,
256
, 301–334 (2002)). As an application, a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups, which generalises the earlier formula of Huang et al. dealing with the particular case when
n
is a prime (
Acta Math. Sin., Engl. Ser.
,
33
, 996–1011 (2017)). As another application, a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve (arXiv preprint, (2007)).</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10114-023-1415-4</doi><tpages>15</tpages></addata></record> |
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| subjects | Graphs Isomorphism Mathematics Mathematics and Statistics Matrices Matrix |
| title | Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices |
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