Extremal graphs for Estrada indices
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/27207 |
Resumo: | Let $\mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $\mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $\mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the family of graphs whose color classes have order not less than a fixed positive integer. The graphs for which the upper bound is tight is obtained. Additionally, an upper bound for the Estrada Index of the complement of a graph in the previous family of graphs with two color classes is given. A Nordhaus-Gaddum type inequality for the Laplacian Estrada index when {$\mathcal{G}$ is a bipartite} graph with color classes of order not less than $2$, is presented. Moreover, a sharp upper bound for the Estrada index of the line graph and for the signless Laplacian index of a graph in terms of connectivity is obtained. |
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Extremal graphs for Estrada indicesEstrada indexSignless Laplacian Estrada indexLaplacian Estrada indexChromatic numberVertex connectivityEdge connectivityLine graphLet $\mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $\mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $\mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the family of graphs whose color classes have order not less than a fixed positive integer. The graphs for which the upper bound is tight is obtained. Additionally, an upper bound for the Estrada Index of the complement of a graph in the previous family of graphs with two color classes is given. A Nordhaus-Gaddum type inequality for the Laplacian Estrada index when {$\mathcal{G}$ is a bipartite} graph with color classes of order not less than $2$, is presented. Moreover, a sharp upper bound for the Estrada index of the line graph and for the signless Laplacian index of a graph in terms of connectivity is obtained.Elsevier2021-03-01T00:00:00Z2020-03-01T00:00:00Z2020-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/27207eng0024-379510.1016/j.laa.2019.10.029Andrade, EnideLenes, EberMallea-Zepeda, ExequielRobbiano, MaríaRodríguez Z., Jonnathaninfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:52:13Zoai:ria.ua.pt:10773/27207Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:50.983355Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Extremal graphs for Estrada indices |
title |
Extremal graphs for Estrada indices |
spellingShingle |
Extremal graphs for Estrada indices Andrade, Enide Estrada index Signless Laplacian Estrada index Laplacian Estrada index Chromatic number Vertex connectivity Edge connectivity Line graph |
title_short |
Extremal graphs for Estrada indices |
title_full |
Extremal graphs for Estrada indices |
title_fullStr |
Extremal graphs for Estrada indices |
title_full_unstemmed |
Extremal graphs for Estrada indices |
title_sort |
Extremal graphs for Estrada indices |
author |
Andrade, Enide |
author_facet |
Andrade, Enide Lenes, Eber Mallea-Zepeda, Exequiel Robbiano, María Rodríguez Z., Jonnathan |
author_role |
author |
author2 |
Lenes, Eber Mallea-Zepeda, Exequiel Robbiano, María Rodríguez Z., Jonnathan |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Andrade, Enide Lenes, Eber Mallea-Zepeda, Exequiel Robbiano, María Rodríguez Z., Jonnathan |
dc.subject.por.fl_str_mv |
Estrada index Signless Laplacian Estrada index Laplacian Estrada index Chromatic number Vertex connectivity Edge connectivity Line graph |
topic |
Estrada index Signless Laplacian Estrada index Laplacian Estrada index Chromatic number Vertex connectivity Edge connectivity Line graph |
description |
Let $\mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $\mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $\mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the family of graphs whose color classes have order not less than a fixed positive integer. The graphs for which the upper bound is tight is obtained. Additionally, an upper bound for the Estrada Index of the complement of a graph in the previous family of graphs with two color classes is given. A Nordhaus-Gaddum type inequality for the Laplacian Estrada index when {$\mathcal{G}$ is a bipartite} graph with color classes of order not less than $2$, is presented. Moreover, a sharp upper bound for the Estrada index of the line graph and for the signless Laplacian index of a graph in terms of connectivity is obtained. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-03-01T00:00:00Z 2020-03-01 2021-03-01T00:00:00Z |
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/10773/27207 |
url |
http://hdl.handle.net/10773/27207 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 10.1016/j.laa.2019.10.029 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137653450342400 |