  The distance energy of a graph $G$ is a recently developed energy-type
invariant, defined as the sum of absolute values of the eigenvalues of the
distance matrix of $G$. There was a vast research for the pairs and families of
non-cospectral graphs having equal distance energy, and most of these
constructions were based on the join of graphs. A graph is called circulant if
it is Cayley graph on the circulant group, i.e. its adjacency matrix is
circulant. A graph is called integral if all eigenvalues of its adjacency
matrix are integers. Integral circulant graphs play an important role in
modeling quantum spin networks supporting the perfect state transfer. In this
paper, we characterize the distance spectra of integral circulant graphs and
prove that these graphs have integral eigenvalues of distance matrix $D$.
Furthermore, we calculate the distance spectra and distance energy of unitary
Cayley graphs. In conclusion, we present two families of pairs $(G_1, G_2)$ of
integral circulant graphs with equal distance energy -- in the first family
$G_1$ is subgraph of $G_2$, while in the second family the diameter of both
graphs is three.
