Limit points of (signless) Laplacian spectral radii of linear trees

Francesco Belardo, Elismar R. Oliveira and Vilmar Trevisan

Applied Mathematics and Computation, 2024, vol. 477, issue C

Abstract: We study limit points of the spectral radii of Laplacian matrices of graphs. We adapted the method used by J. B. Shearer in 1989, devised to prove the density of adjacency limit points of caterpillars, to Laplacian limit points. We show that this fails, in the sense that there is an interval for which the method produces no limit points. Then we generalize the method to Laplacian limit points of linear trees and prove that it generates a larger set of limit points. The results of this manuscript may provide important tools for proving the density of Laplacian limit points in [4.38+,∞).

Keywords: Spectral radius; Tree; Limit points (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002807

DOI: 10.1016/j.amc.2024.128819

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