On cyclically embeddable (n,n−1)-graphs

An embedding of a simple graph G into its complement Ḡ 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−1)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.