On Certain Eigenspaces of Cographs

Abstract

For every cograph there exist bases of the eigenspaces for the eigenvalues $0$ and $-1$ that consist only of vectors with entries from $\{0, 1, -1\}$, a property also exhibited by other graph classes. Moreover, the multiplicities of the eigenvalues $0$ and $-1$ of a cograph can be determined by counting certain vertices of the associated cotree.