Some results about the connectivity of trees
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
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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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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1750318017439334400 |