On the distance spectra of threshold graphs

A graph is called a threshold graph if it does not contain induced C4, P4 or 2K2. Such graphs have numerous applications in computer science and psychology, and they also have nice spectral properties. In this paper, we consider the distance matrix of a connected threshold graph. We show that there are no distance eigenvalues of threshold graphs lying in the interval (−2,−1) and all the eigenvalues, other than −2 or −1, are simple. Besides, we determine all threshold graphs with distinct distance eigenvalues.