The maximal energy of classes of integral circulant graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count nn and a set DD of divisors of nn in such a way that they have vertex set ZnZn and edge set {{a,b}:a,b∈Zn,gcd(a−b,n)∈D}. For a fixed prime power n=psn=ps and a fixed divisor set size |D|=r|D|=r, we analyse the maximal energy among all matching integral circulant graphs. Let pa1