Geodesic
On cyclically embeddable (n,n)-graphs
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 85-104

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An embedding of a simple graph G into its complement G̅ 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.
Keywords: packing of graphs, cyclic permutation 
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Görlich, Agnieszka; Pilśniak, Monika; Woźniak, Mariusz. On cyclically embeddable (n,n)-graphs. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 85-104. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a5/