Some results about the connectivity of trees

Detalhes bibliográficos
Autor(a) principal: Markenzon,Lilian
Data de Publicação: 2013
Outros Autores: Abreu,Nair Maria Maia de, Lee,Luciana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008
Resumo: The second smallest Laplacian eigenvalue of a graph G is called algebraic connectivity, denoted a(G). The ordering of trees via this graph invariant is frequently studied in the literature. In this paper, we present a new invariant, the Internal Degree Sequence (IDS), that also supports an accurate evaluation of the connectivity of trees. We compare the IDS with a(G) for all elements in six classes of trees known to have the largest algebraic connectivity and we show that the IDS provides a strict total ordering of the elements of these classes. This result is also proved for a subclass of trees of diameter 4.
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spelling Some results about the connectivity of treestreesinternal degree sequencealgebraic connectivityThe second smallest Laplacian eigenvalue of a graph G is called algebraic connectivity, denoted a(G). The ordering of trees via this graph invariant is frequently studied in the literature. In this paper, we present a new invariant, the Internal Degree Sequence (IDS), that also supports an accurate evaluation of the connectivity of trees. We compare the IDS with a(G) for all elements in six classes of trees known to have the largest algebraic connectivity and we show that the IDS provides a strict total ordering of the elements of these classes. This result is also proved for a subclass of trees of diameter 4.Sociedade Brasileira de Pesquisa Operacional2013-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008Pesquisa Operacional v.33 n.1 2013reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382013000100008info:eu-repo/semantics/openAccessMarkenzon,LilianAbreu,Nair Maria Maia deLee,Lucianaeng2013-05-24T00:00:00Zoai:scielo:S0101-74382013000100008Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2013-05-24T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv Some results about the connectivity of trees
title Some results about the connectivity of trees
spellingShingle Some results about the connectivity of trees
Markenzon,Lilian
trees
internal degree sequence
algebraic connectivity
title_short Some results about the connectivity of trees
title_full Some results about the connectivity of trees
title_fullStr Some results about the connectivity of trees
title_full_unstemmed Some results about the connectivity of trees
title_sort Some results about the connectivity of trees
author Markenzon,Lilian
author_facet Markenzon,Lilian
Abreu,Nair Maria Maia de
Lee,Luciana
author_role author
author2 Abreu,Nair Maria Maia de
Lee,Luciana
author2_role author
author
dc.contributor.author.fl_str_mv Markenzon,Lilian
Abreu,Nair Maria Maia de
Lee,Luciana
dc.subject.por.fl_str_mv trees
internal degree sequence
algebraic connectivity
topic trees
internal degree sequence
algebraic connectivity
description The second smallest Laplacian eigenvalue of a graph G is called algebraic connectivity, denoted a(G). The ordering of trees via this graph invariant is frequently studied in the literature. In this paper, we present a new invariant, the Internal Degree Sequence (IDS), that also supports an accurate evaluation of the connectivity of trees. We compare the IDS with a(G) for all elements in six classes of trees known to have the largest algebraic connectivity and we show that the IDS provides a strict total ordering of the elements of these classes. This result is also proved for a subclass of trees of diameter 4.
publishDate 2013
dc.date.none.fl_str_mv 2013-04-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-74382013000100008
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.33 n.1 2013
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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