Spectral Radius and Degree Sequence

Hofmeister, M.

doi:10.1002/mana.19881390105

Cited by 85 publications

(28 citation statements)

References 3 publications

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“…If α = 1, then the inequality (2.11) is the bound (2.9) in Remark 2.3. Hence the inequality (2.11) improves and generalizes some known results in [6], [7], [11], [13].…”

Section: P R O O F By a Simple Calculation We Havesupporting

confidence: 79%

“…which is Hofmeister's bound [6] (see also [7], [13]). If α = 1/2, then the inequality (2.11) becomes (2.14)…”

Section: P R O O F By a Simple Calculation We Havementioning

confidence: 96%

“…Up to now, the spectral radius λ 1 (G) and the Laplacian spectral radius µ 1 (G) of G have been extensively investigated for a long time (see, for example, [1], [2], [4], [5], [6], [7], [8], [11], [12], [13] and the references therein). Recently, Liu and Lu [8] introduced two new notations ( α t) i and ( α m) i and obtained some new bounds for the Laplacian spectral radius µ 1 (G) of G. Motivated by this technique, we present some new bounds of λ 1 (G) and µ 1 (G) with parameter α and characterize some extreme graphs which attain these upper bounds.…”

Section: Introductionmentioning

confidence: 99%

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Bounds for the (Laplacian) spectral radius of graphs with parameter α

Tian¹,

Huang²

2012

Czech Math J

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“…If α = 1, then the inequality (2.11) is the bound (2.9) in Remark 2.3. Hence the inequality (2.11) improves and generalizes some known results in [6], [7], [11], [13].…”

Section: P R O O F By a Simple Calculation We Havesupporting

confidence: 79%

“…which is Hofmeister's bound [6] (see also [7], [13]). If α = 1/2, then the inequality (2.11) becomes (2.14)…”

Section: P R O O F By a Simple Calculation We Havementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Bounds for the (Laplacian) spectral radius of graphs with parameter α

Tian¹,

Huang²

2012

Czech Math J

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“…Em Hofmeister (1988), foi determinado um limite inferior para o raio espectral µ(G) em relação à sequência de graus de G. Já existem na literatura diversos resultados sobre a relação entre o raio espectral µ(G) e a sequência de graus de um grafo G. Por exemplo, segue da teoria de matrizes não negativas que o raio espectral satisfaz a desigualdade…”

Section: Desigualdade De Hofmeisterunclassified

Ciclos Hamiltonianos Em Grafos

Santos

2017

CeN

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Resumo Neste trabalho tratamos de um problema clássico bem conhecido em Teoria dos Grafos IntroduçãoA Teoria dos Grafos é um ramo da Matemática que estuda as relações entre os objetos de um determinado conjunto. Para tal estudo, são utilizados estruturas que chamamos de grafos. Seja G = (V,E) um grafo, onde V é um conjunto finito cujos elementos são denominados vértices e E é um conjunto de subconjuntos de dois elementos de V denominados arestas. Podemos representar muitas situações reais através de grafos, por exemplo, a Internet, onde os vértices são os sites e as arestas são links entre os sites. O Facebook também pode ser facilmente modelado por um grafo, cujos vértices são perfis e cujas arestas são relações de amizade.Na

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“…In the literature we could not find any comparable bounds. Besides the folklore result that the spectral radius is at least the average vertex degree in the graph, the first non-trivial lower bound on the spectral radius of a graph was obtained by Hofmeister [12], who showed that the spectral radius is at least the square root of the average squared vertex degrees, i.e., for a graph with vertex degrees d v and spectral radius ρ, the bound ρ diameter was recently obtained in [4]: if the graph is not regular, with maximum vertex degree ∆, then ρ < ∆ − 1 nD . In Section 3, we construct graphs with small spectral radius, showing that the obtained lower bound is asymptotically of the right order.…”

Section: Introductionmentioning

confidence: 99%

A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter

et al. 2008

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General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. a b s t r a c tWe determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.

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Spectral Radius and Degree Sequence

Cited by 85 publications

References 3 publications

Bounds for the (Laplacian) spectral radius of graphs with parameter α

Bounds for the (Laplacian) spectral radius of graphs with parameter α

Ciclos Hamiltonianos Em Grafos

A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter

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