THE EIGENVALUES AND ENERGY OF INTEGRAL CIRCULANT GRAPHS

Abstract. a graph is called circulant if it is a cayley graph on a cyclic group, i.e. its adjacency matrixis circulant. let d be a set of positive, proper divisors of the integer n > 1. the integral circulantgraph icgn(d) has the vertex set zn and the edge set e(icgn(d)) = ffa; bg; gcd(a ?? b; n) 2 dg. letn = p1p2 ... pkm, where p1; p2; ... ; pk are distinct prime numbers and gcd(p1p2 ... pk;m) = 1. the openproblem posed in paper [a. ilic, the energy of unitary cayley graphs, linear algebra appl., 431 (2009)1881{1889] about calculating the energy of an arbitrary integral circulant icgn(d) is completely solvedin this paper, where d = fp1; p2; : : : ; pkg.