Eigenvalue-free interval for threshold graphs

2018/07/26 by Ghorbani, Ebrahim
#05C50 #05C75 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.10302

Abstract

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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