Given a finite group G, we say that a subset C of G is power-closed if, for every \(x\in C\) and \(y\in \langle x\rangle \) with \(\langle x\rangle =\langle y\rangle \) , we have \(y\in C\) . In this paper, we are interested in finite Cayley digraphs \(\textrm{Cay}(G,C)\) over G with connection set C, where C is a union of conjugacy classes of G. We show that each eigenvalue of \(\textrm{Cay}(G,C)\) is integral if and only if C is power-closed. This result will follow from a more general result.
