A lower bound for the energy of hypoenergetic and non hypoenergetic graphs
Autor(a) principal: | |
---|---|
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/10773/27544 |
Resumo: | Let $G$ be a simple undirected graph with $n$ vertices and $m$ edges. The energy of $G,$ $\mathcal{E}(G)$ corresponds to the sum of its singular values. This work obtains lower bounds for $\mathcal{E}(G)$ where one of them generalizes a lower bound obtained by Mc Clelland in $1971$ to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound $2\sqrt{m}$ is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of $G$ is derived. A simple lower bound, which improves the lower bound $2\sqrt{n-1}$, for the energy of trees with $n$ vertices and diameter $d$ is also obtained. |
id |
RCAP_c10b8a431ed3b77bb95c83a367fd772f |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/27544 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphsEnergyHypoenergetic graphNon Hypoenergetic graphLet $G$ be a simple undirected graph with $n$ vertices and $m$ edges. The energy of $G,$ $\mathcal{E}(G)$ corresponds to the sum of its singular values. This work obtains lower bounds for $\mathcal{E}(G)$ where one of them generalizes a lower bound obtained by Mc Clelland in $1971$ to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound $2\sqrt{m}$ is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of $G$ is derived. A simple lower bound, which improves the lower bound $2\sqrt{n-1}$, for the energy of trees with $n$ vertices and diameter $d$ is also obtained.University of Kragujevac, Faculty of Science2020-02-10T17:52:23Z2020-01-01T00:00:00Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/27544eng0340-6253Andrade, EnideR. Carmona, JuanInfante, GeraldineRobbiano, 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:RCAAP2024-02-22T11:52:44Zoai:ria.ua.pt:10773/27544Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:00:03.119975Repositório 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 |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
title |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
spellingShingle |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs Andrade, Enide Energy Hypoenergetic graph Non Hypoenergetic graph |
title_short |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
title_full |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
title_fullStr |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
title_full_unstemmed |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
title_sort |
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs |
author |
Andrade, Enide |
author_facet |
Andrade, Enide R. Carmona, Juan Infante, Geraldine Robbiano, María |
author_role |
author |
author2 |
R. Carmona, Juan Infante, Geraldine Robbiano, María |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Andrade, Enide R. Carmona, Juan Infante, Geraldine Robbiano, María |
dc.subject.por.fl_str_mv |
Energy Hypoenergetic graph Non Hypoenergetic graph |
topic |
Energy Hypoenergetic graph Non Hypoenergetic graph |
description |
Let $G$ be a simple undirected graph with $n$ vertices and $m$ edges. The energy of $G,$ $\mathcal{E}(G)$ corresponds to the sum of its singular values. This work obtains lower bounds for $\mathcal{E}(G)$ where one of them generalizes a lower bound obtained by Mc Clelland in $1971$ to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound $2\sqrt{m}$ is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of $G$ is derived. A simple lower bound, which improves the lower bound $2\sqrt{n-1}$, for the energy of trees with $n$ vertices and diameter $d$ is also obtained. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-02-10T17:52:23Z 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/10773/27544 |
url |
http://hdl.handle.net/10773/27544 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0340-6253 |
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, Faculty of Science |
publisher.none.fl_str_mv |
University of Kragujevac, Faculty of Science |
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 |
|
_version_ |
1799137655142744064 |