Fernando Colman Tura

The minimum number of distinct eigenvalues of a threshold graph is at most $4$

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$(M)\subseteq\{-λ,0,λ,2λ\}$.