Main 𝐐-eigenvalues of quasi-threshold graphs

In this note, we present a structural description of certain connected cographs having k ≥ 2 main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main 𝐐-eigenvalues. In addition, we describe all the quasi-threshold graphs belonging to the subclass of generalized core-satellite graphs with k ≥ 2 main 𝐐-eigenvalues.