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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
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
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
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
Journal Article
by O, Suil
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
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
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
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
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 04/2012, Volume 106, pp. 167 - 177
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
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
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
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
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
Journal Article
Journal of algebraic combinatorics, ISSN 1572-9192, 2018, Volume 50, Issue 1, pp. 99 - 111
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
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
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
Journal Article
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