  The generalized distance matrix of a graph is the matrix whose entries depend
only on the pairwise distances between vertices, and the generalized distance
spectrum is the set of eigenvalues of this matrix. This framework generalizes
many of the commonly studied spectra of graphs. We show that for a large class
of graphs these eigenvalues can be computed explicitly. We also present the
applications of our results to competition models in ecology and rapidly mixing
Markov Chains.
