Several Extreme Coefficients of the Tutte Polynomial of Graphs
Let t i , j be the coefficient of x i y j in the Tutte polynomial T ( G ; x , y ) of a connected bridgeless and loopless graph G with order v and size e . It is trivial that t 0 , e - v + 1 = 1 and t v - 1 , 0 = 1 . In this paper, we obtain expressions for another six extreme coefficients t i , j...
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| Veröffentlicht in: | Graphs and combinatorics 2020-05, Vol.36 (3), p.445-457 |
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| container_title | Graphs and combinatorics |
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| creator | Gong, Helin Jin, Xian’an Li, Mengchen |
| description | Let
t
i
,
j
be the coefficient of
x
i
y
j
in the Tutte polynomial
T
(
G
;
x
,
y
) of a connected bridgeless and loopless graph
G
with order
v
and size
e
. It is trivial that
t
0
,
e
-
v
+
1
=
1
and
t
v
-
1
,
0
=
1
. In this paper, we obtain expressions for another six extreme coefficients
t
i
,
j
’s with
(
i
,
j
)
=
(
0
,
e
-
v
)
,
(
0
,
e
-
v
-
1
)
,
(
v
-
2
,
0
)
,
(
v
-
3
,
0
)
,
(
1
,
e
-
v
)
and
(
v
-
2
,
1
)
in terms of small substructures of
G
. We also discuss their duality properties and their specializations to extreme coefficients of the Jones polynomial. |
| doi_str_mv | 10.1007/s00373-019-02126-y |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2393600959</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2393600959</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-c4a4337a8c1f16f94ce3dd32ee511f5b22ca737c001f0bc60c9b08c661ca6f463</originalsourceid><addsrcrecordid>eNp9kMFKAzEQhoMoWKsv4GnB8-pMspttLoKUWoWCgvUcsunEbml3a5KK-_ZGV_DmaWDm-_-Bj7FLhGsEqG4CgKhEDqhy4Mhl3h-xERaizEuFxTEbgUJMZ1Sn7CyEDQCUWMCI3b7QB3mzzWaf0dOOsmlHzjW2oTaGrHNZXFO2PMRI2XO37dtu1yQ47efe7NfhnJ04sw108TvH7PV-tpw-5Iun-eP0bpFbXkHMbWEKISozsehQOlVYEquV4EQloitrzq2pRGUB0EFtJVhVw8RKidZIV0gxZldD79537wcKUW-6g2_TS82FEhJAlSpRfKCs70Lw5PTeNzvje42gvz3pwZNOnvSPJ92nkBhCIcHtG_m_6n9SX_ElatI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2393600959</pqid></control><display><type>article</type><title>Several Extreme Coefficients of the Tutte Polynomial of Graphs</title><source>SpringerLink Journals</source><creator>Gong, Helin ; Jin, Xian’an ; Li, Mengchen</creator><creatorcontrib>Gong, Helin ; Jin, Xian’an ; Li, Mengchen</creatorcontrib><description>Let
t
i
,
j
be the coefficient of
x
i
y
j
in the Tutte polynomial
T
(
G
;
x
,
y
) of a connected bridgeless and loopless graph
G
with order
v
and size
e
. It is trivial that
t
0
,
e
-
v
+
1
=
1
and
t
v
-
1
,
0
=
1
. In this paper, we obtain expressions for another six extreme coefficients
t
i
,
j
’s with
(
i
,
j
)
=
(
0
,
e
-
v
)
,
(
0
,
e
-
v
-
1
)
,
(
v
-
2
,
0
)
,
(
v
-
3
,
0
)
,
(
1
,
e
-
v
)
and
(
v
-
2
,
1
)
in terms of small substructures of
G
. We also discuss their duality properties and their specializations to extreme coefficients of the Jones polynomial.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-019-02126-y</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Coefficients ; Combinatorics ; Engineering Design ; Mathematics ; Mathematics and Statistics ; Original Paper ; Polynomials ; Substructures</subject><ispartof>Graphs and combinatorics, 2020-05, Vol.36 (3), p.445-457</ispartof><rights>Springer Japan KK, part of Springer Nature 2020</rights><rights>Springer Japan KK, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-c4a4337a8c1f16f94ce3dd32ee511f5b22ca737c001f0bc60c9b08c661ca6f463</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/s00373-019-02126-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-019-02126-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Gong, Helin</creatorcontrib><creatorcontrib>Jin, Xian’an</creatorcontrib><creatorcontrib>Li, Mengchen</creatorcontrib><title>Several Extreme Coefficients of the Tutte Polynomial of Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Let
t
i
,
j
be the coefficient of
x
i
y
j
in the Tutte polynomial
T
(
G
;
x
,
y
) of a connected bridgeless and loopless graph
G
with order
v
and size
e
. It is trivial that
t
0
,
e
-
v
+
1
=
1
and
t
v
-
1
,
0
=
1
. In this paper, we obtain expressions for another six extreme coefficients
t
i
,
j
’s with
(
i
,
j
)
=
(
0
,
e
-
v
)
,
(
0
,
e
-
v
-
1
)
,
(
v
-
2
,
0
)
,
(
v
-
3
,
0
)
,
(
1
,
e
-
v
)
and
(
v
-
2
,
1
)
in terms of small substructures of
G
. We also discuss their duality properties and their specializations to extreme coefficients of the Jones polynomial.</description><subject>Coefficients</subject><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Polynomials</subject><subject>Substructures</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKAzEQhoMoWKsv4GnB8-pMspttLoKUWoWCgvUcsunEbml3a5KK-_ZGV_DmaWDm-_-Bj7FLhGsEqG4CgKhEDqhy4Mhl3h-xERaizEuFxTEbgUJMZ1Sn7CyEDQCUWMCI3b7QB3mzzWaf0dOOsmlHzjW2oTaGrHNZXFO2PMRI2XO37dtu1yQ47efe7NfhnJ04sw108TvH7PV-tpw-5Iun-eP0bpFbXkHMbWEKISozsehQOlVYEquV4EQloitrzq2pRGUB0EFtJVhVw8RKidZIV0gxZldD79537wcKUW-6g2_TS82FEhJAlSpRfKCs70Lw5PTeNzvje42gvz3pwZNOnvSPJ92nkBhCIcHtG_m_6n9SX_ElatI</recordid><startdate>20200501</startdate><enddate>20200501</enddate><creator>Gong, Helin</creator><creator>Jin, Xian’an</creator><creator>Li, Mengchen</creator><general>Springer Japan</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>20200501</creationdate><title>Several Extreme Coefficients of the Tutte Polynomial of Graphs</title><author>Gong, Helin ; Jin, Xian’an ; Li, Mengchen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-c4a4337a8c1f16f94ce3dd32ee511f5b22ca737c001f0bc60c9b08c661ca6f463</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Coefficients</topic><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Polynomials</topic><topic>Substructures</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gong, Helin</creatorcontrib><creatorcontrib>Jin, Xian’an</creatorcontrib><creatorcontrib>Li, Mengchen</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>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gong, Helin</au><au>Jin, Xian’an</au><au>Li, Mengchen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Several Extreme Coefficients of the Tutte Polynomial of Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2020-05-01</date><risdate>2020</risdate><volume>36</volume><issue>3</issue><spage>445</spage><epage>457</epage><pages>445-457</pages><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Let
t
i
,
j
be the coefficient of
x
i
y
j
in the Tutte polynomial
T
(
G
;
x
,
y
) of a connected bridgeless and loopless graph
G
with order
v
and size
e
. It is trivial that
t
0
,
e
-
v
+
1
=
1
and
t
v
-
1
,
0
=
1
. In this paper, we obtain expressions for another six extreme coefficients
t
i
,
j
’s with
(
i
,
j
)
=
(
0
,
e
-
v
)
,
(
0
,
e
-
v
-
1
)
,
(
v
-
2
,
0
)
,
(
v
-
3
,
0
)
,
(
1
,
e
-
v
)
and
(
v
-
2
,
1
)
in terms of small substructures of
G
. We also discuss their duality properties and their specializations to extreme coefficients of the Jones polynomial.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-019-02126-y</doi><tpages>13</tpages></addata></record> |
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| ispartof | Graphs and combinatorics, 2020-05, Vol.36 (3), p.445-457 |
| issn | 0911-0119 1435-5914 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Coefficients Combinatorics Engineering Design Mathematics Mathematics and Statistics Original Paper Polynomials Substructures |
| title | Several Extreme Coefficients of the Tutte Polynomial of Graphs |
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