On the energy of singular and non singular graphs
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10773/27220 |
Resumo: | Let $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $\rho$ and nullity $\kappa$. The energy of $G,$ $\mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $\mathcal{E}(G)$ in terms of the coefficient of $\mu^{\kappa}$ in the expansion of characteristic polynomial, $p(\mu)=\det{(\mu I-A)}$ are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in $2013$ to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound $2\rho.$ Considering an increasing sequence convergent to $\rho$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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On the energy of singular and non singular graphsEnergySingular graphsNon singular graphsLet $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $\rho$ and nullity $\kappa$. The energy of $G,$ $\mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $\mathcal{E}(G)$ in terms of the coefficient of $\mu^{\kappa}$ in the expansion of characteristic polynomial, $p(\mu)=\det{(\mu I-A)}$ are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in $2013$ to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound $2\rho.$ Considering an increasing sequence convergent to $\rho$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed.University of Kragujevac2019-12-19T18:52:28Z2020-01-01T00:00:00Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/27220eng0340-6253http://match.pmf.kg.ac.rs/content83n3.htmAndrade, EnideCarmona, Juan R.Poveda, AlexRobbiano, Maríainfo: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:RCAAP2024-02-22T11:52:43Zoai:ria.ua.pt:10773/27220Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:00:02.909465Repositório 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 |
On the energy of singular and non singular graphs |
title |
On the energy of singular and non singular graphs |
spellingShingle |
On the energy of singular and non singular graphs Andrade, Enide Energy Singular graphs Non singular graphs |
title_short |
On the energy of singular and non singular graphs |
title_full |
On the energy of singular and non singular graphs |
title_fullStr |
On the energy of singular and non singular graphs |
title_full_unstemmed |
On the energy of singular and non singular graphs |
title_sort |
On the energy of singular and non singular graphs |
author |
Andrade, Enide |
author_facet |
Andrade, Enide Carmona, Juan R. Poveda, Alex Robbiano, María |
author_role |
author |
author2 |
Carmona, Juan R. Poveda, Alex Robbiano, María |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Andrade, Enide Carmona, Juan R. Poveda, Alex Robbiano, María |
dc.subject.por.fl_str_mv |
Energy Singular graphs Non singular graphs |
topic |
Energy Singular graphs Non singular graphs |
description |
Let $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $\rho$ and nullity $\kappa$. The energy of $G,$ $\mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $\mathcal{E}(G)$ in terms of the coefficient of $\mu^{\kappa}$ in the expansion of characteristic polynomial, $p(\mu)=\det{(\mu I-A)}$ are obtained. In particular one of the bounds generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in $2013$ to the case of graphs with given nullity. The bipartite case is also studied obtaining in this case, a sufficient condition to improve the spectral lower bound $2\rho.$ Considering an increasing sequence convergent to $\rho$ a convergent increasing sequence of lower bounds for the energy of $G$ is constructed. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-12-19T18:52:28Z 2020-01-01T00:00:00Z 2020-01-01 |
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/10773/27220 |
url |
http://hdl.handle.net/10773/27220 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0340-6253 http://match.pmf.kg.ac.rs/content83n3.htm |
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 |
University of Kragujevac |
publisher.none.fl_str_mv |
University of Kragujevac |
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) |
collection |
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 |
repository.mail.fl_str_mv |
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1799137655132258304 |