For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph. 

For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.