A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs

DOI10.1016/j.laa.2005.06.024zbMath1072.05039OpenAlexW2024386879MaRDI QIDQ2568992

Ravindra B. Bapat, Kinkar Chandra Das

Publication date: 17 October 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2005.06.024

zbMATH Keywords

largest eigenvalueLaplacian matrix

Mathematics Subject Classification ID

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

Related Items (15)

NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS ⋮ A Unified Framework for Structured Graph Learning via Spectral Constraints ⋮ The spectral radius of maximum weighted cycle ⋮ Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs ⋮ A nontrivial upper bound on the largest Laplacian eigenvalue of weighted graphs ⋮ On the signless Laplacian spectral radius of weighted digraphs ⋮ Bounds for the largest Laplacian eigenvalue of weighted graphs ⋮ On the bounds for the largest Laplacian eigenvalues of weighted graphs ⋮ A sharp upper bound on the spectral radius of weighted graphs ⋮ Extremal graph characterization from the bounds of the spectral radius of weighted graphs ⋮ On the spectral radius of weighted trees with given number of pendant vertices and a positive weight set ⋮ Lower bounds on the (Laplacian) spectral radius of weighted graphs ⋮ On the Laplacian spectral radius of weighted trees with fixed diameter and weight set ⋮ On the spectral radius of weighted unicyclic graphs with a positive weight set ⋮ Bounds on the spectral radii of digraphs in terms of walks

Cites Work

• A note on Laplacian graph eigenvalues
• On the Laplacian eigenvalues of a graph
• A new upper bound for eigenvalues of the Laplacian matrix of a graph
• An improved upper bound for Laplacian graph eigenvalues
• A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs.
• An always nontrivial upper bound for Laplacian graph eigenvalues
• Sharp lower bounds on the Laplacian eigenvalues of trees
• Sharp upper bounds for the Laplacian graph eigenvalues
• Eigenvalues of the Laplacian of a graph^∗
• The Laplacian Spectrum of a Graph II
• The largest two Laplacian eigenvalues of a graph
• Matrix theory. Basic results and techniques
• de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph

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