In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most 4. Moreover, given any threshold graph G and any nonzero real number λ, we explicitly construct a matrix M associated with G such that DSpec(M)⊆{−λ,0,λ,2λ}.
@article{arxiv.2505.13024,
title = {The minimum number of distinct eigenvalues of a threshold graph is at most $4$},
author = {Luiz Emilio Allem and Carlos Hoppen and João Lazzarin and Lucas Siviero Sibemberg and Fernando Colman Tura},
journal= {arXiv preprint arXiv:2505.13024},
year = {2025}
}