Eigenvalue-free interval for threshold graphs

Eigenvalue-free interval for threshold graphs

This paper deals with the eigenvalues of the adjacency matrices of threshold graphs for which −1 and 0 are considered as trivial eigenvalues. We show that threshold graphs have no non-trivial eigenvalues in the interval [(−1−2)/2,(−1+2)/2]. This confirms a conjecture by Aguilar, Lee, Piato, and Schw...

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Veröffentlicht in:Linear algebra and its applications 2019-12, Vol.583, p.300-305
1. Verfasser: Ghorbani, Ebrahim
Format: Artikel
Sprache:eng
Schlagworte:
Anti-regular graph
Eigenvalue
Eigenvalues
Graphs
Linear algebra
Threshold graph
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Zusammenfassung:This paper deals with the eigenvalues of the adjacency matrices of threshold graphs for which −1 and 0 are considered as trivial eigenvalues. We show that threshold graphs have no non-trivial eigenvalues in the interval [(−1−2)/2,(−1+2)/2]. This confirms a conjecture by Aguilar, Lee, Piato, and Schweitzer (2018).
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.08.028