Some results about the connectivity of trees

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...

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Main Authors:	Lilian Markenzon, Nair Maria Maia de Abreu, Luciana Lee
Format:	Article
Language:	English
Published:	Sociedade Brasileira de Pesquisa Operacional 2013-04-01
Series:	Pesquisa Operacional
Subjects:	trees internal degree sequence algebraic connectivity
Online Access:	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008&lng=en&tlng=en

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spelling	doaj-9040411074f7499b964c0ba6464665cb2020-11-24T22:29:39ZengSociedade Brasileira de Pesquisa OperacionalPesquisa Operacional1678-51422013-04-0133112313210.1590/S0101-74382013000100008S0101-74382013000100008Some results about the connectivity of treesLilian Markenzon0Nair Maria Maia de Abreu1Luciana Lee2Universidade Federal do Rio de JaneiroUniversidade Federal do Rio de JaneiroUniversidade Federal de Mato GrossoThe 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008&lng=en&tlng=entreesinternal degree sequencealgebraic connectivity
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lilian Markenzon Nair Maria Maia de Abreu Luciana Lee
spellingShingle	Lilian Markenzon Nair Maria Maia de Abreu Luciana Lee Some results about the connectivity of trees Pesquisa Operacional trees internal degree sequence algebraic connectivity
author_facet	Lilian Markenzon Nair Maria Maia de Abreu Luciana Lee
author_sort	Lilian Markenzon
title	Some results about the connectivity of trees
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
publisher	Sociedade Brasileira de Pesquisa Operacional
series	Pesquisa Operacional
issn	1678-5142
publishDate	2013-04-01
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.
topic	trees internal degree sequence algebraic connectivity
url	http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382013000100008&lng=en&tlng=en
work_keys_str_mv	AT lilianmarkenzon someresultsabouttheconnectivityoftrees AT nairmariamaiadeabreu someresultsabouttheconnectivityoftrees AT lucianalee someresultsabouttheconnectivityoftrees
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Some results about the connectivity of trees

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