A Laplacian eigenbasis for threshold graphs

A Laplacian eigenbasis for threshold graphs

Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs t...

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Bibliographic Details
Main Authors: Macharete Rafael R., Del-Vecchio Renata R., Teixeira Heber, de Lima Leonardo
Format: Article
Language:English
Published: De Gruyter 2024-10-01
Series:Special Matrices
Subjects:
threshold graph
spectral characterization
laplacian matrix
weakly hadamard diagonalizable graph
05c50
05c35
Online Access:https://doi.org/10.1515/spma-2024-0029
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Summary:Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs that are weakly Hadamard diagonalizable.
ISSN:2300-7451

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