The energy of integral circulant graphs with prime power order

Abstract

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 {{a, b}: a, b ∈ Zn, gcd (a - b,n) ∈ D}. For an integral circulant graph on ps 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.