  The distance matrix of a graph $G$ is the matrix containing the pairwise
distances between vertices. The distance eigenvalues of $G$ are the eigenvalues
of its distance matrix and they form the distance spectrum of $G$. We determine
the distance spectra of halved cubes, double odd graphs, and Doob graphs,
completing the determination of distance spectra of distance regular graphs
having exactly one positive distance eigenvalue. We characterize strongly
regular graphs having more positive than negative distance eigenvalues. We give
examples of graphs with few distinct distance eigenvalues but lacking
regularity properties. We also determine the determinant and inertia of the
distance matrices of lollipop and barbell graphs.
