Packing of graphs and permutations

An embedding of a graph G (into its complement G) is a permutation Δ on V(G) such that if an edge xy belongs to E(G) then Δ(x)Δ(y) does not belong to E(G). If there exists an embedding of G we say that G is embeddable or that there is a packing of two copies of the graph G into complete graph Kn. s paper we discuss a variety of results, some quite recent, concerning the relationships between the embeddings of graphs in their complements and the structure of the embedding permutations.