Results 41 to 50 of about 2,028,246 (339)
On the spectral radius of trees
Linear Algebra and its Applications, 2001 AbstractIn this paper, we investigated the spectral radius of trees and obtained the following result: Let T be a tree on n vertices. Let M(T) denote one maximum matching of T and |M(T)|=i. Let Ti* be a tree as shown in Fig. 1. Thenρ(T)⩽12(n−i+1+(n−i+1)2−4(n−2i+1)),and equality holds if and only if T=Ti*.
Tan Shang Wang, Guo Ji Ming
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Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius [PDF]
Physical Review Research, 2019 A common difficulty in applications of machine learning is the lack of any general principle for guiding the choices of key parameters of the underlying neural network.
Junjie Jiang, Y. Lai
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On the spectral radius of graphs
Linear Algebra and its Applications, 2004 AbstractLet G be a simple undirected graph. For v∈V(G), the 2-degree of v is the sum of the degrees of the vertices adjacent to v. Denote by ρ(G) and μ(G) the spectral radius of the adjacency matrix and the Laplacian matrix of G, respectively. In this paper, we present two lower bounds of ρ(G) and μ(G) in terms of the degrees and the 2-degrees of ...
Aimei Yu, Feng Tian, Mei Lu
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On the Signless Laplacian Spectral Radius of Graphs without Small Books and Intersecting Quadrangles
Mathematics, 2022 In this paper, we determine the maximum signless Laplacian spectral radius of all graphs which do not contain small books as a subgraph and characterize all extremal graphs. In addition, we give an upper bound of the signless Laplacian spectral radius of
Ming-Zhu Chen +3 more
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, 2022 minor additions, 15 pages, to be submitted to a Springer volume in memory of Jean ...
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Inequalities for numerical invariants of sets of matrices [PDF]
, 2002 We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger and Wang as an ...
Berger +11 more
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Spectral radius of bipartite graphs [PDF]
Linear Algebra and its Applications, 2015 Let k, p, q be positive integers with k < p < q+1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph Kp,q of bipartition orders p and q by deleting k edges is attained when the deleting edges are all incident on a common vertex which is located in the partite set of order q.
Chih-wen Weng, Chia An Liu
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Spectral radius of semi-Hilbertian space operators and its applications [PDF]
Annals of Functional Analysis, 2019 In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
Kais Feki
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Some inequalities on the spectral radius of nonnegative tensors
Open Mathematics, 2020 The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.
Ma Chao +3 more
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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices
Special Matrices, 2021 Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely.
Chen Chaohui +2 more
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