THE ENERGY OF INTEGRAL CIRCULANT GRAPHS WITH PRIME POWER ORDER

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 Z(n) and its edge set is {{a, b} : a, b is an element of Z(n), gcd(a - b, n) is an element of D}. 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 fixed p(s) and varying divisor sets D.