On the algebraic connectivity of some caterpillars: A sharp upper bound and a total ordering

Rojo, Óscar; Medina, Luis; Abreu, Nair Maria Maia de; Justel, Cláudia Marcela

doi:10.1016/j.laa.2009.09.007

Cited by 11 publications

(5 citation statements)

References 14 publications

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“…The algebraic technique uses classical tools from matrix theory to analyze and obtain properties of the characteristic polynomial of the trees involved. Prototype papers that use this algebraic approach are [6,9].…”

Section: Statement Of the Results And Proof Techniquesmentioning

confidence: 99%

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Algebraic connectivity on a subclass of caterpillars

Rojo

Rocha

Trevisan

2011

Electronic Notes in Discrete Mathematics

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Section: Statement Of the Results And Proof Techniquesmentioning

confidence: 99%

“…We easily see that any caterpillar in C has n vertices and diameter d. In [9], we give a total ordering by algebraic connectivity on the subclasses…”

Section: Introductionmentioning

confidence: 99%

Algebraic connectivity on a subclass of caterpillars

Rojo

Rocha

Trevisan

2011

Electronic Notes in Discrete Mathematics

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“…It is among the most important Laplacian eigenvalues. In recent years, the algebraic connectivity has received much attention, see [11,36,37] and the references cited therein. A graph is connected if and only if µ > 0.…”

Section: An Application To Signless Laplacian Estrada Indexmentioning

confidence: 99%

Graphs with maximum Laplacian and signless Laplacian Estrada index

Gutman

Medina

Pizarro

et al. 2016

Discrete Mathematics

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a b s t r a c tThe Laplacian Estrada index (LEE) and the signless Laplacian Estrada index (SLEE) of a graph G are, respectively, the sum of the exponentials of the eigenvalues of the Laplacian and signless Laplacian matrix of G. The vertex frustration index υ b of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. Graphs having maximum LEE and SLEE values are determined among graphs with n vertices and 1 ≤ υ b ≤ n − 3.

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“…Among the most important Laplacian eigenvalues is the algebraic connectivity of G, defined as the second smallest Laplacian eigenvalue µ n−1 , [10]. Recently, the algebraic connectivity has received much attention, see [1,19,22,23] and the references cited therein. A graph is connected if and only if µ n−1 > 0, [10].…”

Section: Notation and Preliminaresmentioning

confidence: 99%