The eigenvalues and energy of integral circulant graphs

A graph is called textit{circulant} if it is a Cayley graph on acyclic group, i.e. its adjacency matrix is circulant. Let $D$ be aset of positive, proper divisors of the integer $n>1$. Theintegral circulant graph $ICG_{n}(D)$ has the vertex set$mathbb{Z}_{n}$ and the edge set E$(ICG_{n}(D))= {{a,b};gcd(a-b,n)in D }$. Let $n=p_{1}p_{2}cdots p_{k}m$, where$p_{1},p_{2},cdots,p_{k}$ are distinct prime numbers and$gcd(p_{1}p_{2}cdots p_{k},m)=1$. The open problem posed in paper[A. Ili'{c}, The energy of unitary Cayley graphs, Linear AlgebraAppl., 431 (2009) 1881--1889] about calculating the energy of anarbitrary integral circulant $ICG_{n}(D)$ is completely solved inthis paper, where $D={p_{1},p_{2},ldots,p_{k} } $.