On cyclically embeddable (n, n)-graphs

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n, n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.