Document Type: Original Manuscript


Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, 16785–136, 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 derangement
graph 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.