Appl. Anal. Discrete Math. 5 (2011), 22{36. doi:10.2298/AADM110131003S THE ENERGY OF INTEGRAL CIRCULANT GRAPHS WITH PRIME POWER

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. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is ffa; bg: a; b 2 Zn; gcd(a b; n) 2 Dg: For an integral circulant graph on p s vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D: Moreover, we study minimal and maximal energies for xed ps and varying divisor sets D: 1