The role of the anti-regular graph in the spectral analysis of threshold graphs
| Autor: | Matthew Ficarra, Brittany Sullivan, Cesar O. Aguilar, Natalie Schurman |
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| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Threshold graph Algebra and Number Theory Conjecture 010102 general mathematics Spectral properties Interlacing 010103 numerical & computational mathematics 01 natural sciences Graph Combinatorics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Regular graph Spectral analysis Combinatorics (math.CO) Geometry and Topology 0101 mathematics Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 588:210-223 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2019.12.005 |
| Popis: | 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 anti-regular 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 a strengthened version of the recently proved fact that no threshold graph contains an eigenvalue in the interval Ω = [ − 1 − 2 2 , − 1 + 2 2 ] , 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. |
| Databáze: | OpenAIRE |
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