Geodesic
On cyclically embeddable graphs
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 241-248

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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 some families of embeddable graphs such that the corresponding permutation is cyclic.
Keywords: packing of graphs, unicyclic graphs, cyclic permutation 
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Woźniak, Mariusz. On cyclically embeddable graphs. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 241-248. http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a10/