Integral cographs and applications

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we show a cograph that has a balanced cotree $T_G(a_1,\dots ,a_{r-1},0\mathrm{\mid }0,\dots ,0,a_r)$ is integral computing its spectrum. As an application, these integral cographs can be used to estimate the eigenvalues of any cograph.