A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs.

DOI10.1016/j.laa.2003.06.009zbMath1042.05059OpenAlexW1997900391MaRDI QIDQ1415294

Kinkar Chandra Das

Publication date: 3 December 2003

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.06.009

zbMATH Keywords

Laplacian matrixGraphUpper boundLargest eigenvalue

Mathematics Subject Classification ID

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

Related Items (26)

NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS ⋮ Automated conjectures on upper bounds for the largest Laplacian eigenvalue of graphs ⋮ Extremal graph characterization from the upper bound of the Laplacian spectral radius of weighted graphs ⋮ Sharp upper bounds on the signless Laplacian spectral radius of strongly connected digraphs ⋮ A nontrivial upper bound on the largest Laplacian eigenvalue of weighted graphs ⋮ Characterization of graphs having extremal Randić indices ⋮ Spectral properties of complex unit gain graphs ⋮ Mysteries around the graph Laplacian eigenvalue 4 ⋮ Proof of conjectures involving algebraic connectivity of graphs ⋮ On the bounds for the largest Laplacian eigenvalues of weighted graphs ⋮ On the conjecture for certain Laplacian integral spectrum of graphs ⋮ Sharp upper and lower bounds for the Laplacian spectral radius and the spectral radius of graphs ⋮ Spectra of quaternion unit gain graphs ⋮ Several sharp upper bounds for the largest Laplacian eigenvalue of a graph ⋮ A sharp upper bound for the number of spanning trees of a graph ⋮ A survey of automated conjectures in spectral graph theory ⋮ On upper bounds for Laplacian graph eigenvalues ⋮ On conjectures involving second largest signless Laplacian eigenvalue of graphs ⋮ Bounds on the index of the signless Laplacian of a graph ⋮ The Laplacian spectrum of a graph ⋮ A new upper bound for the Laplacian spectral radius of graphs ⋮ Characterization on graphs which achieve a Das' upper bound for Laplacian spectral radius ⋮ A sharp upper bound for the spectral radius of a nonnegative matrix and applications ⋮ The case of equality in the Dobrushin-Deutsch-Zenger bound ⋮ A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs ⋮ Bounds for the Laplacian spectral radius of graphs

Cites Work

• A note on Laplacian graph eigenvalues
• An improved upper bound for Laplacian graph eigenvalues
• An always nontrivial upper bound for Laplacian graph eigenvalues
• Sharp upper bounds for the Laplacian graph eigenvalues
• Eigenvalues of the Laplacian of a graph^∗
• The Laplacian Spectrum of a Graph II
• de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph

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