Spectral properties of a class of cographs

Santanu Mandal, Ranjit Mehatari

Published 2022-12-14Version 1

We explore several properties of the adjacency matrix of a class of connected cographs. Those cographs can be defined by a finite sequence of natural numbers. Using that sequence we obtain multiplicity of the eigenvalues $0,-1$, inertia for the adjacency matrix of the cograph under consideration. We find an eigenvalue-free interval for such graphs which is better than previously obtained interval $(-1,0)$. Finally, we establish a suitable formula for the characteristic polynomial of the adjacency matrix for such graphs.