  The covering spectrum is a geometric invariant of a Riemannian manifold, more
generally of a metric space, that measures the size of its one-dimensional
holes by isolating a portion of the length spectrum. In a previous paper we
demonstrated that the covering spectrum is not a spectral invariant of a
manifold in dimensions three and higher. In this article we give an example of
two isospectral Cayley graphs that admit length space structures with distinct
covering spectra. From this we deduce the existence of infinitely many pairs of
Sunada-isospectral surfaces with unequal covering spectra.
