Modjtaba Ghorbani - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, ۱۶۷۸۵–۱۳۶, Tehran, Iran.
Mina Rajabi-Parsa - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, ۱۶۷۸۵–۱۳۶, Tehran, Iran.

A permutation with no fixed points is called a derangement. The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement. Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

permutation groups, graph eigenvalues, Frobenius group