Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions

Bibliographic Details
Main Author: Cardoso, Domingos M.
Publication Date: 2023
Other Authors: Costa, Inês Serôdio, Duarte, Rui
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/39411
Summary: Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the n-Queens graph Q(n) is equal to −4 for every n ≥ 4 and it is also proven that the multiplicity of this eigenvalue is (n−3)^2. Finally, edge clique partitions of additional infinite families of connected graphs and their relations with the least eigenvalues are presented.
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spelling Sharp bounds on the least eigenvalue of a graph determined from edge clique partitionsLeast eigenvalue of a graphEdge clique partitionn-Queens graphSharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the n-Queens graph Q(n) is equal to −4 for every n ≥ 4 and it is also proven that the multiplicity of this eigenvalue is (n−3)^2. Finally, edge clique partitions of additional infinite families of connected graphs and their relations with the least eigenvalues are presented.Springer2023-09-20T10:53:28Z2023-08-01T00:00:00Z2023-08info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39411eng0925-989910.1007/s10801-023-01247-1Cardoso, Domingos M.Costa, Inês SerôdioDuarte, Ruiinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:47:01Zoai:ria.ua.pt:10773/39411Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:20:15.658553Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
title Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
spellingShingle Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
Cardoso, Domingos M.
Least eigenvalue of a graph
Edge clique partition
n-Queens graph
title_short Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
title_full Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
title_fullStr Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
title_full_unstemmed Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
title_sort Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
author Cardoso, Domingos M.
author_facet Cardoso, Domingos M.
Costa, Inês Serôdio
Duarte, Rui
author_role author
author2 Costa, Inês Serôdio
Duarte, Rui
author2_role author
author
dc.contributor.author.fl_str_mv Cardoso, Domingos M.
Costa, Inês Serôdio
Duarte, Rui
dc.subject.por.fl_str_mv Least eigenvalue of a graph
Edge clique partition
n-Queens graph
topic Least eigenvalue of a graph
Edge clique partition
n-Queens graph
description Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the n-Queens graph Q(n) is equal to −4 for every n ≥ 4 and it is also proven that the multiplicity of this eigenvalue is (n−3)^2. Finally, edge clique partitions of additional infinite families of connected graphs and their relations with the least eigenvalues are presented.
publishDate 2023
dc.date.none.fl_str_mv 2023-09-20T10:53:28Z
2023-08-01T00:00:00Z
2023-08
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/39411
url http://hdl.handle.net/10773/39411
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0925-9899
10.1007/s10801-023-01247-1
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
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reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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