Lower bounds of the Laplacian spectrum of graphs based on diameter

DOI10.1016/j.laa.2006.07.023zbMath1106.05064OpenAlexW2129259584MaRDI QIDQ861000

Feng Tian, Mei Lu, Lian Zhu Zhang

Publication date: 9 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.07.023

zbMATH Keywords

algebraic connectivity

Mathematics Subject Classification ID

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

Related Items (11)

Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities ⋮ New conjectures on algebraic connectivity and the Laplacian spread of graphs ⋮ On the bounds of Laplacian eigenvalues of k-connected graphs ⋮ Bounds for the Kirchhoff index via majorization techniques ⋮ A lower bound for algebraic connectivity based on the connection-graph-stability method ⋮ Proof of conjectures involving algebraic connectivity of graphs ⋮ Ordering trees with algebraic connectivity and diameter ⋮ Lower bounds for the Laplacian spectral radius of graphs ⋮ Eigenvalues and diameter ⋮ On relation between Kirchhoff index, Laplacian-energy-like invariant and Laplacian energy of graphs ⋮ Bounds for the Laplacian spectral radius of graphs

Cites Work

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• \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
• A note on Laplacian graph eigenvalues
• On the Laplacian eigenvalues of a graph
• Eigenvalues, diameter, and mean distance in graphs
• Laplacian matrices of graphs: A survey
• An always nontrivial upper bound for Laplacian graph eigenvalues
• Matrix Analysis
• Diameters and Eigenvalues
• A bound on the algebraic connectivity of a graph in terms of the number of cutpoints
• Characteristic vertices of trees^*

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