Linear Algebra and Its Applications, ISSN 0024-3795, 10/2015, Volume 482, pp. 158 - 190

In 1993 Hong asked what are the best bounds on the k'th largest eigenvalue λk(G) of a graph G of order n...

Ky Fan norms of graphs | k'th largest singular eigenvalue of a graph | Spectral Nordhaus–Gaddum problems | k'th largest eigenvalue of a graph | Spectral Nordhaus-Gaddum problems | MATHEMATICS | MATHEMATICS, APPLIED | SUM

Ky Fan norms of graphs | k'th largest singular eigenvalue of a graph | Spectral Nordhaus–Gaddum problems | k'th largest eigenvalue of a graph | Spectral Nordhaus-Gaddum problems | MATHEMATICS | MATHEMATICS, APPLIED | SUM

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 05/2018, Volume 34, Issue 3, pp. 395 - 414

.... Let denote the eigenvalues of D(G). In this paper, we characterize all connected graphs...

The second least distance eigenvalue | The third largest distance eigenvalue | Distance matrix | MATHEMATICS | REGULAR GRAPHS | DISTINCT EIGENVALUES | SPECTRA

The second least distance eigenvalue | The third largest distance eigenvalue | Distance matrix | MATHEMATICS | REGULAR GRAPHS | DISTINCT EIGENVALUES | SPECTRA

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 03/2018, Volume 129, pp. 55 - 78

We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenvalue at most 1.

Three distinct eigenvalues | Second largest eigenvalue | Nonregular graphs | Strongly regular graphs | MATHEMATICS | Mathematics - Combinatorics

Three distinct eigenvalues | Second largest eigenvalue | Nonregular graphs | Strongly regular graphs | MATHEMATICS | Mathematics - Combinatorics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2019, Volume 259, pp. 153 - 159

For a connected graph G with order n and an integer k≥1, we denote by Sk(D(G))=λ1(D(G))+⋯+λk(D(G)) the sum of k largest distance eigenvalues of G...

The second largest distance eigenvalue | Distance eigenvalue | Eigenvalue sum | Distance matrix | MATHEMATICS, APPLIED | REMOTENESS | CONJECTURE | Eigenvalues | Lower bounds | Graphs | Upper bounds | Eigen values

The second largest distance eigenvalue | Distance eigenvalue | Eigenvalue sum | Distance matrix | MATHEMATICS, APPLIED | REMOTENESS | CONJECTURE | Eigenvalues | Lower bounds | Graphs | Upper bounds | Eigen values

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2016, Volume 491, pp. 4 - 14

Let G be a d-regular multigraph, and let λ2(G) be the second largest eigenvalue of G...

Edge-connectivity | Second largest eigenvalue | Regular multigraphs | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Combinatorics

Edge-connectivity | Second largest eigenvalue | Regular multigraphs | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Combinatorics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 21, pp. 2858 - 2866

In this paper, we first give an upper bound for the largest signless Laplacian eigenvalue of a graph and find all the extremal graphs...

Friendship graph | Signless Laplacian | Graph index | Spectral characterization | Largest eigenvalue | Cospectral graphs | MATHEMATICS | SPECTRAL-RADIUS | Eigenvalues | Graphs | Spectra | Mathematical analysis | Upper bounds

Friendship graph | Signless Laplacian | Graph index | Spectral characterization | Largest eigenvalue | Cospectral graphs | MATHEMATICS | SPECTRAL-RADIUS | Eigenvalues | Graphs | Spectra | Mathematical analysis | Upper bounds

Journal Article

The Annals of statistics, ISSN 0090-5364, 2008, Volume 36, Issue 6, pp. 2638 - 2716

.... The distribution of the largest eigenvalue of (A + B)⁻¹ B has numerous applications in multivariate statistics, but is difficult to calculate exactly...

Hypergeometric functions | Approximation | Differential equations | Eigenvalues | Sine function | Polynomials | Matrices | Covariance matrices | Weighting functions | Jacobi polynomials | Roy's test | Soft edge | Multivariate analysis of variance, random matrix theory | Liouville-Green | Largest root | Characteristic roots | Canonical correlation analysis | Traey-Widom distribution | Fredholm determinant | characteristic roots | UNIVERSALITY | largest root | SPACING DISTRIBUTIONS | multivariate analysis of variance | STATISTICS & PROBABILITY | soft edge | UNITARY | random matrix theory | Tracy-Widom distribution | ORTHOGONAL POLYNOMIALS | ASYMPTOTICS | SPECTRUM | EDGE | Roy’s test | Liouville–Green | 15A52 | Tracy–Widom distribution | 62E20 | 62H10

Hypergeometric functions | Approximation | Differential equations | Eigenvalues | Sine function | Polynomials | Matrices | Covariance matrices | Weighting functions | Jacobi polynomials | Roy's test | Soft edge | Multivariate analysis of variance, random matrix theory | Liouville-Green | Largest root | Characteristic roots | Canonical correlation analysis | Traey-Widom distribution | Fredholm determinant | characteristic roots | UNIVERSALITY | largest root | SPACING DISTRIBUTIONS | multivariate analysis of variance | STATISTICS & PROBABILITY | soft edge | UNITARY | random matrix theory | Tracy-Widom distribution | ORTHOGONAL POLYNOMIALS | ASYMPTOTICS | SPECTRUM | EDGE | Roy’s test | Liouville–Green | 15A52 | Tracy–Widom distribution | 62E20 | 62H10

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 07/2017, Volume 63, Issue 7, pp. 4521 - 4531

We derive the probability that all eigenvalues of a random matrix M lie within an arbitrary interval [a, b], ψ(a, b) Pr{a λ min (M), λ max (M) b...

Symmetric matrices | Limiting | Random matrix theory | Gaussian orthogonal ensemble | Covariance matrices | Physics | Wishart matrices | Jacobian matrices | eigenvalues distribution | Eigenvalues and eigenfunctions | Tracy-Widom distribution | Jacobi ensemble | MANOVA | Compressed sensing | principal component analysis | Eigenvalues distribution | Principal component analysis | LARGEST ROOT | UNIVERSALITY | CAPACITY | compressed sensing | APPROXIMATION | ENSEMBLES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | DISTRIBUTIONS | SYSTEMS | MULTIVARIATE-ANALYSIS | Usage | Random matrices | Analysis of covariance | Symmetric functions | Eigenvalues | Eigenfunctions | Matrices | Research | Gaussian distribution | Mathematical analysis | Matrix methods | Eigen values

Symmetric matrices | Limiting | Random matrix theory | Gaussian orthogonal ensemble | Covariance matrices | Physics | Wishart matrices | Jacobian matrices | eigenvalues distribution | Eigenvalues and eigenfunctions | Tracy-Widom distribution | Jacobi ensemble | MANOVA | Compressed sensing | principal component analysis | Eigenvalues distribution | Principal component analysis | LARGEST ROOT | UNIVERSALITY | CAPACITY | compressed sensing | APPROXIMATION | ENSEMBLES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | DISTRIBUTIONS | SYSTEMS | MULTIVARIATE-ANALYSIS | Usage | Random matrices | Analysis of covariance | Symmetric functions | Eigenvalues | Eigenfunctions | Matrices | Research | Gaussian distribution | Mathematical analysis | Matrix methods | Eigen values

Journal Article

The Annals of statistics, ISSN 0090-5364, 2018, Volume 46, Issue 5, pp. 2186 - 2215

... distribution of the first k largest eigenvalues of B when x(t) is nonstationary. As an application, two new unit root tests for possible nonstationarity of high-dimensional...

Linear process | Unit root test | Largest eigenvalue | Asymptotic normality | POPULATION | UNIVERSALITY | unit root test | STATISTICS | EQUATIONS | STATISTICS & PROBABILITY | linear process | LIMIT | MODEL | DISTRIBUTIONS | PANEL-DATA | largest eigenvalue | SAMPLE COVARIANCE MATRICES

Linear process | Unit root test | Largest eigenvalue | Asymptotic normality | POPULATION | UNIVERSALITY | unit root test | STATISTICS | EQUATIONS | STATISTICS & PROBABILITY | linear process | LIMIT | MODEL | DISTRIBUTIONS | PANEL-DATA | largest eigenvalue | SAMPLE COVARIANCE MATRICES

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2016, Volume 504, pp. 462 - 467

.... It is shown that mck(G)≤k−1k(m−μmin(G)n2), where μmin(G) is the smallest eigenvalue of the adjacency matrix of G...

Largest eigenvalues | Largest Laplacian eigenvalue | Smallest adjacency eigenvalue | Max k-cut | Chromatic number | MATHEMATICS | MATHEMATICS, APPLIED | School construction

Largest eigenvalues | Largest Laplacian eigenvalue | Smallest adjacency eigenvalue | Max k-cut | Chromatic number | MATHEMATICS | MATHEMATICS, APPLIED | School construction

Journal Article

Journal of Multivariate Analysis, ISSN 0047-259X, 04/2012, Volume 106, pp. 167 - 177

In the spiked population model introduced by Johnstone (2001) [11], the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes...

Extreme eigenvalues | Sample covariance matrices | Largest eigenvalue | Central limit theorems | Spiked population model | Secondary | Primary | LARGE WIGNER MATRICES | LIMITING SPECTRAL DISTRIBUTION | DIMENSIONAL RANDOM MATRICES | CONVERGENCE | STATISTICS & PROBABILITY | DEFORMATION | COVARIANCE MATRICES | Sample covariance matrices Spiked population model Central limit theorems Largest eigenvalue Extreme eigenvalues

Extreme eigenvalues | Sample covariance matrices | Largest eigenvalue | Central limit theorems | Spiked population model | Secondary | Primary | LARGE WIGNER MATRICES | LIMITING SPECTRAL DISTRIBUTION | DIMENSIONAL RANDOM MATRICES | CONVERGENCE | STATISTICS & PROBABILITY | DEFORMATION | COVARIANCE MATRICES | Sample covariance matrices Spiked population model Central limit theorems Largest eigenvalue Extreme eigenvalues

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2010, Volume 432, Issue 9, pp. 2214 - 2221

Let k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e ( G ) + k + 1 2 , where e ( G...

Laplacian eigenvalues of a graph | Largest eigenvalue | Sum of eigenvalues | MATHEMATICS | MATHEMATICS, APPLIED | Computer science | Universities and colleges

Laplacian eigenvalues of a graph | Largest eigenvalue | Sum of eigenvalues | MATHEMATICS | MATHEMATICS, APPLIED | Computer science | Universities and colleges

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2014, Volume 457, pp. 400 - 407

This paper finds a new and improved geometric bound for the second largest eigenvalue of a random walk Markov chain on an undirected graph.

Markov chain | Undirected graph | Second largest eigenvalue | Random walk | MATHEMATICS, APPLIED | Markov processes

Markov chain | Undirected graph | Second largest eigenvalue | Random walk | MATHEMATICS, APPLIED | Markov processes

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 8

Let G be a simple connected graph of order n, where . Its normalized Laplacian eigenvalues...

Analysis | bound | normalized Laplacian eigenvalue | Mathematics, general | Mathematics | Applications of Mathematics | largest eigenvalue | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Lower bounds | Graphs | Inequalities

Analysis | bound | normalized Laplacian eigenvalue | Mathematics, general | Mathematics | Applications of Mathematics | largest eigenvalue | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Lower bounds | Graphs | Inequalities

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 11

... ≠ j $i\neq j$ , whose ij-entry is r i j $r_{ij}$ . In this paper, we determine the eigenvalues of the resistance-distance matrix of complete multipartite graphs...

largest resistance-distance eigenvalue | Analysis | resistance-distance matrix | Mathematics, general | resistance distance | Mathematics | Applications of Mathematics | second largest resistance-distance eigenvalue | MATHEMATICS | MATHEMATICS, APPLIED | COBWEB | VERTEX JOIN | EDGE JOIN | Eigenvalues | Optimization techniques | Lower bounds | Graphs | Upper bounds | Research

largest resistance-distance eigenvalue | Analysis | resistance-distance matrix | Mathematics, general | resistance distance | Mathematics | Applications of Mathematics | second largest resistance-distance eigenvalue | MATHEMATICS | MATHEMATICS, APPLIED | COBWEB | VERTEX JOIN | EDGE JOIN | Eigenvalues | Optimization techniques | Lower bounds | Graphs | Upper bounds | Research

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 12

In this paper, we present two S-type Z-eigenvalue inclusion sets involved with a nonempty proper subset S of N for general tensors...

largest Z-eigenvalue | weakly symmetric nonnegative tensors | Z-eigenvalue inclusion sets | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BOUNDS | LOCALIZATION SET | Mathematical analysis | Upper bounds | Tensors | Research | 15A69 | 15A18

largest Z-eigenvalue | weakly symmetric nonnegative tensors | Z-eigenvalue inclusion sets | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | BOUNDS | LOCALIZATION SET | Mathematical analysis | Upper bounds | Tensors | Research | 15A69 | 15A18

Journal Article

Journal of algebraic combinatorics, ISSN 1572-9192, 2018, Volume 50, Issue 1, pp. 99 - 111

... ) , ( 1 , j , i ) ∣ 2 ≤ i < j ≤ n } and $$T_3=\{(i,j,k),(i,k,j)\mid 1\le i 05C50 | Second largest eigenvalue | Convex and Discrete Geometry | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Cayley graph | Alternating group graph | MATHEMATICS | AUTOMORPHISM GROUP | Mathematics - Combinatorics

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2015, Volume 484, pp. 504 - 539

The authors' monograph Spectral Generalizations of Line Graphs was published in 2004, following the successful use of star complements to complete the classification of graphs with least eigenvalue −2...

Hoffman graph | Star complement | Graph spectra | Signed graph | signless Laplacian | MATHEMATICS, APPLIED | GENERALIZED LINE GRAPHS | COSPECTRAL GRAPHS | FAT HOFFMAN GRAPHS | STAR COMPLEMENTS | SIGNED GRAPHS | 2ND LARGEST EIGENVALUE | MATHEMATICS | VERTEX-DELETED SUBGRAPHS | BIPARTITE INTEGRAL GRAPHS | SMALLEST EIGENVALUE

Hoffman graph | Star complement | Graph spectra | Signed graph | signless Laplacian | MATHEMATICS, APPLIED | GENERALIZED LINE GRAPHS | COSPECTRAL GRAPHS | FAT HOFFMAN GRAPHS | STAR COMPLEMENTS | SIGNED GRAPHS | 2ND LARGEST EIGENVALUE | MATHEMATICS | VERTEX-DELETED SUBGRAPHS | BIPARTITE INTEGRAL GRAPHS | SMALLEST EIGENVALUE

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2010, Volume 432, Issue 11, pp. 3018 - 3029

... ) . In this paper we obtain a lower bound on the second largest signless Laplacian eigenvalue and an upper bound on the smallest signless Laplacian eigenvalue of G . In [5], Cvetković et al...

Graph | Signless Laplacian matrix | Algebraic connectivity | Laplacian matrix | The second largest signless Laplacian eigenvalue | The largest signless Laplacian eigenvalue | Smallest signless Laplacian eigenvalue | MATHEMATICS, APPLIED | BOUNDS | MATRICES | INTEGRAL GRAPHS | SPECTRUM | ALKANES | Questions and answers

Graph | Signless Laplacian matrix | Algebraic connectivity | Laplacian matrix | The second largest signless Laplacian eigenvalue | The largest signless Laplacian eigenvalue | Smallest signless Laplacian eigenvalue | MATHEMATICS, APPLIED | BOUNDS | MATRICES | INTEGRAL GRAPHS | SPECTRUM | ALKANES | Questions and answers

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2015, Volume 467, pp. 100 - 115

.... Moreover, we prove two conjectures involving the second largest eigenvalue of the distance signless Laplacian matrix Q(G) of graph G.

Distance signless Laplacian matrix | Graph | The second largest eigenvalue of the distance signless Laplacian matrix | Distance signless Laplacian spectral radius | MATHEMATICS | MATHEMATICS, APPLIED

Distance signless Laplacian matrix | Graph | The second largest eigenvalue of the distance signless Laplacian matrix | Distance signless Laplacian spectral radius | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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