Extremal energies of integral circulant graphs via multiplicativity

AbstractThe energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. Integral circulant graphs can be characterised by their order n and a set D of positive divisors of n in such a way that they have vertex set Z/nZ and edge set {(a,b):a,b∈Z/nZ,gcd(a-b,n)∈D}. Among integral circulant graphs of fixed prime power order ps, those having minimal energy Eminps or maximal energy Emaxps, respectively, are known. We study the energy of integral circulant graphs of arbitrary order n with so-called multiplicative divisor sets. This leads to good bounds for Eminn and Emaxn as well as conjectures concerning the true value of Eminn