Nonorientable regular embeddings of graphs of order pq

In [ J. Algeb. Combin. 19 (2004), 123–141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q . In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q . Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq .