2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226793New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley graphs of cyclic groups with the same list of eigenvalues of their adjacency matrices will be presented.27 pages, 1 figureCombinatorics05C50; 05C60text