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The energy of a graph is the sum of the moduli of the eigenvalues of itsadjacency matrix. We study the energy of integral circulant graphs, also calledgcd graphs, which can be characterized by their vertex count n and a set D ofdivisors 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 studythe maximal energy among all integral circulant graphs of prime power order psand varying divisor sets D. Our main result states that this maximal energyapproximately lies between s(p - 1)p^(s-1) and twice this value. We constructsuitable divisor sets for which the energy lies in this interval. We alsocharacterize hyperenergetic integral circulant graphs of prime power order andexhibit an interesting topological property of their divisor sets.

Integral circulant graphs of prime power order with maximal energy