An Interlacing Property of the Signless Laplacian of Threshold Graphs

We show that for threshold graphs, the eigenvalues of the signless Laplacian matrix interlace with the degrees of the vertices. As an application, we show that the signless Brouwer conjecture holds for threshold graphs, i.e., for threshold graphs the sum of the $k$ largest eigenvalues is bounded by...

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Published inThe Electronic journal of combinatorics Vol. 32; no. 1
Main Authors Helmberg, Christoph, Porto, Guilherme, Torres, Guilherme, Trevisan, Vilmar
Format Journal Article
LanguageEnglish
Published 28.02.2025
Online AccessGet full text
ISSN1077-8926
1077-8926
DOI10.37236/12332

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Abstract We show that for threshold graphs, the eigenvalues of the signless Laplacian matrix interlace with the degrees of the vertices. As an application, we show that the signless Brouwer conjecture holds for threshold graphs, i.e., for threshold graphs the sum of the $k$ largest eigenvalues is bounded by the number of edges plus $k + 1$ choose $2$.
AbstractList We show that for threshold graphs, the eigenvalues of the signless Laplacian matrix interlace with the degrees of the vertices. As an application, we show that the signless Brouwer conjecture holds for threshold graphs, i.e., for threshold graphs the sum of the $k$ largest eigenvalues is bounded by the number of edges plus $k + 1$ choose $2$.
Author Trevisan, Vilmar
Helmberg, Christoph
Torres, Guilherme
Porto, Guilherme
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Snippet We show that for threshold graphs, the eigenvalues of the signless Laplacian matrix interlace with the degrees of the vertices. As an application, we show that...
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Title An Interlacing Property of the Signless Laplacian of Threshold Graphs
Volume 32
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