  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 n and a set D of
divisors of n in such a way that they have vertex set Zn and edge set {{a, b} :
a, b in Zn; gcd(a - b, n) in D}. Using tools from convex optimization, we study
the maximal energy among all integral circulant graphs of prime power order ps
and varying divisor sets D. Our main result states that this maximal energy
approximately lies between s(p - 1)p^(s-1) and twice this value. We construct
suitable divisor sets for which the energy lies in this interval. We also
characterize hyperenergetic integral circulant graphs of prime power order and
exhibit an interesting topological property of their divisor sets.
