Strongly Regular Integral Circulant Graphs and Their Energies

Let S ⊂ Zn be a finite cyclic group of order n > 1. Assume that 0 / ∈ S and −S = {−s : s ∈ S} = S. The circulant graph G = Cir(n, S) is the undirected graph having the vertex set V (G) = Zn and edge set E(G) = {ab : a, b ∈ Zn, a− b ∈ S}. Let D be a set of positive, proper divisors of the integer n. We characterize certain strongly regular integral circulant graphs with energy 2n(1− 1/d) for a fixed d ∈ D , d > 1.