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Paper   IPM / M / 16032
School of Mathematics
  Title:   Eigenvalue-free interval for threshold graphs
  Author(s):  Ebrahim Ghorbani
  Status:   Publishied
  Journal: Linear Algebra Appl.
  Vol.:  583
  Year:  2019
  Pages:   300-305
  Supported by:  IPM
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).

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