Uniform upper bound of the second largest eigenvalue of stochastic matrices with equal-neighbor rule

2017 ◽  
Vol 354 (14) ◽  
pp. 6033-6043
Author(s):  
Chao Huang ◽  
Changbin Yu
Keyword(s):  
Upper Bound ◽  
Stochastic Matrices ◽  
Largest Eigenvalue ◽  
Second Largest Eigenvalue

Log-Concavity and the Spectral Gap of Stochastic Matrices

1997 ◽  
Vol 6 (3) ◽  
pp. 371-379
Author(s):  
EKKEHARD WEINECK
Keyword(s):  
Characteristic Polynomial ◽  
Spectral Gap ◽  
Stochastic Matrix ◽  
Identity Matrix ◽  
Combinatorial Approach ◽  
Stochastic Matrices ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
Second Largest Eigenvalue

Let Q be a stochastic matrix and I be the identity matrix. We show by a direct combinatorial approach that the coefficients of the characteristic polynomial of the matrix I−Q are log-concave. We use this fact to prove a new bound for the second-largest eigenvalue of Q.

Some spectral properties of Aα-matrix

2019 ◽  
Vol 11 (06) ◽  
pp. 1950070
Author(s):  
Shuang Zhang ◽  
Yan Zhu
Keyword(s):  
Real Number ◽  
Spectral Radius ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Spectral Properties ◽  
Upper Bounds ◽  
Largest Eigenvalue ◽  
Number Formula ◽  
Second Largest Eigenvalue ◽  
Spectral Radius Formula

For a real number [Formula: see text], the [Formula: see text]-matrix of a graph [Formula: see text] is defined to be [Formula: see text] where [Formula: see text] and [Formula: see text] are the adjacency matrix and degree diagonal matrix of [Formula: see text], respectively. The [Formula: see text]-spectral radius of [Formula: see text], denoted by [Formula: see text], is the largest eigenvalue of [Formula: see text]. In this paper, we consider the upper bound of the [Formula: see text]-spectral radius [Formula: see text], also we give some upper bounds for the second largest eigenvalue of [Formula: see text]-matrix.

Graphs with the second signless Laplacian eigenvalue ≤ 4

2021 ◽  
Vol 10 (1) ◽  
pp. 131-152
Author(s):  
Stephen Drury
Keyword(s):  
General Solution ◽  
Knapsack Problem ◽  
Laplacian Eigenvalue ◽  
Simple Graphs ◽  
Largest Eigenvalue ◽  
Signless Laplacian ◽  
Second Largest Eigenvalue

Abstract We discuss the question of classifying the connected simple graphs H for which the second largest eigenvalue of the signless Laplacian Q(H) is ≤ 4. We discover that the question is inextricable linked to a knapsack problem with infinitely many allowed weights. We take the first few steps towards the general solution. We prove that this class of graphs is minor closed.

On the estimation of the second largest eigenvalue of Markov ciphers

2016 ◽  
pp. n/a-n/a
Author(s):  
Weijia Xue ◽  
Tingting Lin ◽  
Xin Shun ◽  
Fenglei Xue ◽  
Xuejia Lai
Keyword(s):  
Largest Eigenvalue ◽  
Second Largest Eigenvalue

scholarly journals On graphs whose second largest eigenvalue does not exceed (√5−1)2

1995 ◽  
Vol 138 (1-3) ◽  
pp. 213-227 ◽  
Author(s):  
Dragoš Cvetković ◽  
Slobodan Simić
Keyword(s):  
Largest Eigenvalue ◽  
Second Largest Eigenvalue
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