Bounding the largest eigenvalue of trees in terms of the largest vertex degree

DOI10.1016/S0024-3795(02)00442-1zbMath1028.05062OpenAlexW1999392855MaRDI QIDQ1863520

Dragan Stevanović

Publication date: 11 March 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(02)00442-1

zbMATH Keywords

treelargest eigenvalueLaplacian matrixadajancy matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (28)

The spectra of some trees and bounds for the largest eigenvalue of any tree ⋮ Strong-coupling scales and the graph structure of multi-gravity theories ⋮ An explicit formula for eigenvalues of Bethe trees and upper bounds on the largest eigenvalue of any tree ⋮ The largest eigenvalue of unicyclic graphs ⋮ On the eigenvalues and spectral radius of starlike trees ⋮ Laplacian matching polynomial of graphs ⋮ Reciprocal distance Laplacian spectral properties double stars and their complements ⋮ Mysteries around the graph Laplacian eigenvalue 4 ⋮ New upper bounds on the spectral radius of trees with the given number of vertices and maximum degree ⋮ Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues ⋮ The Laplacian spectral radii of trees with degree sequences ⋮ A relation between the signless Laplacian spectral radius of complete multipartite graphs and majorization ⋮ Laplacian spectral radius of trees with given maximum degree ⋮ Ordering trees by their largest eigenvalues ⋮ New upper bounds on the spectral radius of unicyclic graphs ⋮ On the \(A_{\alpha}\)-spectra of trees ⋮ Ordering trees by their Laplacian spectral radii ⋮ Improved bounds for the largest eigenvalue of trees ⋮ Resolution of AutoGraphiX conjectures relating the index and matching number of graphs ⋮ Largest \(H\)-eigenvalue of uniform \(s\)-hypertrees ⋮ Majorization and the spectral radius of starlike trees ⋮ The least eigenvalue of graphs with given connectivity ⋮ Matrix norms and rapid mixing for spin systems ⋮ Sharp lower bounds on the Laplacian eigenvalues of trees ⋮ On the location of zeros of the Laplacian matching polynomials of graphs ⋮ Bounds for the Laplacian spectral radius of graphs ⋮ On the α-spectral radius of graphs ⋮ On the spectral radius of trees with fixed diameter

Cites Work

• Laplacian matrices of graphs: A survey
• A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph
• Theory of monomer-dimer systems
• On the eigenvalues of trees
• Eigenvalues of the Laplacian of a graph^∗
• The Laplacian Spectrum of a Graph II
• The largest eigenvalue of a graph: A survey
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Bounding the largest eigenvalue of trees in terms of the largest vertex degree