On the multiplicity of Laplacian eigenvalues for unicyclic graphs
Let G be a connected graph of order n and U a unicyclic graph with the same order. We firstly give a sharp bound for m G ( μ ), the multiplicity of a Laplacian eigenvalue μ of G . As a straightforward result, m U (1) ⩽ n − 2. We then provide two graph operations (i.e., grafting and shifting) on grap...
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| Veröffentlicht in: | Czechoslovak Mathematical Journal 2022, Vol.72 (2), p.371-390 |
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| container_title | Czechoslovak Mathematical Journal |
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| creator | Wen, Fei Huang, Qiongxiang |
| description | Let
G
be a connected graph of order
n
and
U
a unicyclic graph with the same order. We firstly give a sharp bound for
m
G
(
μ
), the multiplicity of a Laplacian eigenvalue
μ
of
G
. As a straightforward result,
m
U
(1) ⩽
n
− 2. We then provide two graph operations (i.e., grafting and shifting) on graph
G
for which the value of
m
G
(1) is nondecreasing. As applications, we get the distribution of
m
U
(1) for unicyclic graphs on
n
vertices. Moreover, for the two largest possible values of
m
U
(1) ∈ {
n
− 5,
n
− 3}, the corresponding graphs
U
are completely determined. |
| doi_str_mv | 10.21136/CMJ.2022.0499-20 |
| format | Article |
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G
be a connected graph of order
n
and
U
a unicyclic graph with the same order. We firstly give a sharp bound for
m
G
(
μ
), the multiplicity of a Laplacian eigenvalue
μ
of
G
. As a straightforward result,
m
U
(1) ⩽
n
− 2. We then provide two graph operations (i.e., grafting and shifting) on graph
G
for which the value of
m
G
(1) is nondecreasing. As applications, we get the distribution of
m
U
(1) for unicyclic graphs on
n
vertices. Moreover, for the two largest possible values of
m
U
(1) ∈ {
n
− 5,
n
− 3}, the corresponding graphs
U
are completely determined.</description><identifier>ISSN: 0011-4642</identifier><identifier>EISSN: 1572-9141</identifier><identifier>DOI: 10.21136/CMJ.2022.0499-20</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Apexes ; Convex and Discrete Geometry ; Eigenvalues ; Graphs ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations</subject><ispartof>Czechoslovak Mathematical Journal, 2022, Vol.72 (2), p.371-390</ispartof><rights>Institute of Mathematics, Czech Academy of Sciences 2022</rights><rights>Institute of Mathematics, Czech Academy of Sciences 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-5fd8827b664081bc34479eb39ae4311b9513cbaeb01eb1b8b678400b62f1c91f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.21136/CMJ.2022.0499-20$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.21136/CMJ.2022.0499-20$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Wen, Fei</creatorcontrib><creatorcontrib>Huang, Qiongxiang</creatorcontrib><title>On the multiplicity of Laplacian eigenvalues for unicyclic graphs</title><title>Czechoslovak Mathematical Journal</title><addtitle>Czech Math J</addtitle><description>Let
G
be a connected graph of order
n
and
U
a unicyclic graph with the same order. We firstly give a sharp bound for
m
G
(
μ
), the multiplicity of a Laplacian eigenvalue
μ
of
G
. As a straightforward result,
m
U
(1) ⩽
n
− 2. We then provide two graph operations (i.e., grafting and shifting) on graph
G
for which the value of
m
G
(1) is nondecreasing. As applications, we get the distribution of
m
U
(1) for unicyclic graphs on
n
vertices. Moreover, for the two largest possible values of
m
U
(1) ∈ {
n
− 5,
n
− 3}, the corresponding graphs
U
are completely determined.</description><subject>Analysis</subject><subject>Apexes</subject><subject>Convex and Discrete Geometry</subject><subject>Eigenvalues</subject><subject>Graphs</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><issn>0011-4642</issn><issn>1572-9141</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQhi0EEqXwAGyWmFN8tuPYY1UBBRV1gdmyjdO6SpNgJ0h9e1yKxMR0N3z_f6cPoVsgMwrAxP3i9WVGCaUzwpUqKDlDEygrWijgcI4mhAAUXHB6ia5S2hFCGHA5QfN1i4etx_uxGULfBBeGA-5qvDJ9Y1wwLfZh49sv04w-4bqLeGyDO7hM4k00_TZdo4vaNMnf_M4pen98eFssi9X66XkxXxWOCjkUZf0hJa2sEJxIsI5xXilvmTKeMwCrSmDOGm8JeAtWWlFJTogVtAanoGZTdHfq7WP3mZ8Z9K4bY5tPairKspSKUZopOFEudilFX-s-hr2JBw1E_5jS2ZQ-mtJHU3nLGXrKpMy2Gx__mv8PfQMdQmqn</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Wen, Fei</creator><creator>Huang, Qiongxiang</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2022</creationdate><title>On the multiplicity of Laplacian eigenvalues for unicyclic graphs</title><author>Wen, Fei ; Huang, Qiongxiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-5fd8827b664081bc34479eb39ae4311b9513cbaeb01eb1b8b678400b62f1c91f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Apexes</topic><topic>Convex and Discrete Geometry</topic><topic>Eigenvalues</topic><topic>Graphs</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wen, Fei</creatorcontrib><creatorcontrib>Huang, Qiongxiang</creatorcontrib><collection>CrossRef</collection><jtitle>Czechoslovak Mathematical Journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wen, Fei</au><au>Huang, Qiongxiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the multiplicity of Laplacian eigenvalues for unicyclic graphs</atitle><jtitle>Czechoslovak Mathematical Journal</jtitle><stitle>Czech Math J</stitle><date>2022</date><risdate>2022</risdate><volume>72</volume><issue>2</issue><spage>371</spage><epage>390</epage><pages>371-390</pages><issn>0011-4642</issn><eissn>1572-9141</eissn><abstract>Let
G
be a connected graph of order
n
and
U
a unicyclic graph with the same order. We firstly give a sharp bound for
m
G
(
μ
), the multiplicity of a Laplacian eigenvalue
μ
of
G
. As a straightforward result,
m
U
(1) ⩽
n
− 2. We then provide two graph operations (i.e., grafting and shifting) on graph
G
for which the value of
m
G
(1) is nondecreasing. As applications, we get the distribution of
m
U
(1) for unicyclic graphs on
n
vertices. Moreover, for the two largest possible values of
m
U
(1) ∈ {
n
− 5,
n
− 3}, the corresponding graphs
U
are completely determined.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.21136/CMJ.2022.0499-20</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0011-4642 |
| ispartof | Czechoslovak Mathematical Journal, 2022, Vol.72 (2), p.371-390 |
| issn | 0011-4642 1572-9141 |
| language | eng |
| recordid | cdi_proquest_journals_2655589322 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Analysis Apexes Convex and Discrete Geometry Eigenvalues Graphs Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations |
| title | On the multiplicity of Laplacian eigenvalues for unicyclic graphs |
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