نتایج جستجو برای: largest eigenvalue

تعداد نتایج: 109243  

Journal: :Communications in mathematics and statistics 2021

Abstract We offer a new method for proving that the maxima eigenvalue of normalized graph Laplacian with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 - provided not complete and equality attained if only com...

2003
Fan Chung Linyuan Lu

Many graphs arising in various information networks exhibit the “power law” behavior – the number of vertices of degree k is proportional to k−β for some positive β. We show that if β > 2.5, the largest eigenvalue of a random power law graph is almost surely (1+o(1)) √ m where m is the maximum degree. When 2 < β < 2.5, the largest eigenvalue is heavily concentrated at cm3−β for some constant c ...

Journal: :Discrete Mathematics 2008
Shu-Guang Guo

Denote by Tn,q the set of trees with n vertices and matching number q. Guo [On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] gave the tree in Tn,q with the greatest value of the largest Laplacian eigenvalue. In this paper, we give another proof of this result. Using our method, we can go further beyond Guo by giving the tree in Tn,q with the second largest va...

2016
XIAOLING MA Ioan Tomescu

The family G of connected graphs with second largest Laplacian eigenvalue at most θ, where θ = 3.2470 is the largest root of the equation μ−5μ+6μ−1 = 0, is characterized by Wu, Yu and Shu [Y.R. Wu, G.L. Yu and J.L. Shu, Graphs with small second largest Laplacian eigenvalue, European J. Combin. 36 (2014) 190–197]. Let G(a, b, c, d) be a graph with order n = 2a + b + 2c + 3d + 1 that consists of ...

Journal: :Combinatorics, Probability & Computing 2002
Vladimir Nikiforov

Combinatorics, Probability & Computing / Volume 11 / Issue 02 / March 2002, pp 179 189 DOI: 10.1017/S0963548301004928, Published online: 25 April 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301004928 How to cite this article: V. NIKIFOROV (2002). Some Inequalities for the Largest Eigenvalue of a Graph. Combinatorics, Probability & Computing, 11, pp 179-189 doi:10.1...

Journal: :iranian journal of mathematical chemistry 2015
a. maden e. kaya

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

2007
A. E. Brouwer

There are 11 integral trees with largest eigenvalue 3.

Journal: :Physical review letters 2011
Daniel B Larremore Woodrow L Shew Juan G Restrepo

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenv...

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