On the Eigenvalues Distribution in Threshold Graphs

Lou, Zhenzhen; Wang, Jianfeng; Huang, Qiongxiang

doi:10.1007/s00373-019-02042-1

Cited by 8 publications

(2 citation statements)

References 20 publications

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“…It was also conjectured that among all threshold graphs on n vertices, A n has the smallest positive eigenvalue and the largest negative eigenvalue less than −1. In [15], the authors use the quotient graph associated to the degree partition (which is an equitable partition [8]) of a threshold graph to derive the known results on the inertia of a threshold graph and determine which threshold graphs have distinct eigenvalues. Finally, in [14] the authors derive an explicit expression for the characteristic polynomial of a threshold graph and use it to find the determinant of A(G) and prove that no two non-isomorphic graphs are cospectral.…”

Section: Introductionmentioning

confidence: 99%

The role of the anti-regular graph in the spectral analysis of threshold graphs

Aguilar

Ficarra

Schurman

et al. 2020

Linear Algebra and its Applications

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The purpose of this paper is to highlight the role played by the anti-regular graph within the class of threshold graphs. Using the fact that every threshold graph contains a maximal antiregular graph, we show that some known results, and new ones, on the spectral properties of threshold graphs can be deduced from (i) the known results on the eigenvalues of anti-regular graphs, (ii) the subgraph structure of threshold graphs, and (iii) eigenvalue interlacing. In particular, we prove that no threshold graph contains an eigenvalue in the interval Ω =], except possibly the trivial eigenvalues −1 and/or 0, determine the inertia of a threshold graph, and give partial results on a conjecture regarding the optimality of the non-trivial eigenvalues of an anti-regular graph within the class of threshold graphs.

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Section: Introductionmentioning

confidence: 99%

The role of the anti-regular graph in the spectral analysis of threshold graphs

Aguilar

Ficarra

Schurman

et al. 2020

Linear Algebra and its Applications

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“…In [8] was proved that no threshold graph has eigenvalues in the interval (−1, 0). For more spectral properties we suggest consulting the articles [1,2,3,5,9,10].…”

Section: Introductionmentioning

confidence: 99%

A conjecture of eigenvalues of threshold graphs

Tura¹

2020

Preprint

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Let An be the anti-regular graph of order n. It was conjectured that among all threshold graphs on n vertices, An has the smallest positive eigenvalue and the largest eigenvalue less than −1. Recently, in [1] was given partial results for this conjecture and identified the critical cases where a more refined method is needed. In this paper, we deal with these cases and confirm that conjecture holds.

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Laplacian eigenvalues of weighted threshold graphs

Andelic,

Stanić

2024

Comp. Appl. Math.

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On the Eigenvalues Distribution in Threshold Graphs

Cited by 8 publications

References 20 publications

The role of the anti-regular graph in the spectral analysis of threshold graphs

The role of the anti-regular graph in the spectral analysis of threshold graphs

A conjecture of eigenvalues of threshold graphs

Laplacian eigenvalues of weighted threshold graphs

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