Extremal energies of integral circulant graphs via multiplicativity

Abstract: The 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 of positive divisors of n in such a way that they have vertex set and edge set . Among integral circulant graphs of fixed prime power order , those having minimal energy or maximal energy , 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 and as well as conjectures concerning the true value of . [Copyright &y& Elsevier]