Most Laplacian eigenvalues of a tree are small

2019/06/29 by Jacobs, David P., Oliveira, Elismar R., Trevisan, Vilmar · 4 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.00234

Abstract

We show that the number of Laplacian eigenvalues greater than the average degree of a tree having n vertices is at most \lfloor(n)/(2) \rfloor.

Cited by

• Spectral properties of the deformed Laplacian matrix of trees and H-join graphs
• Laplacian Spectrum and Domination in Trees
• On the distribution of A_α-eigenvalues in terms of graph invariants
• Girth and Laplacian eigenvalue distribution

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