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Discussiones Mathematicae Graph Theory 23(1) (2003) 85-104
DOI: https://doi.org/10.7151/dmgt.1187

ON CYCLICALLY EMBEDDABLE (n,n)-GRAPHS

Agnieszka Görlich, Monika Pilśniak and Mariusz Woźniak

Faculty of Applied Mathematics AGH
Department of Discrete Mathematics
al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: Forys@uci.agh.edu.pl, Pilsniak@uci.agh.edu.pl, MWozniak@uci.agh.edu.pl

Abstract

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.

Keywords: packing of graphs, cyclic permutation.

2000 Mathematics Subject Classification: 05C70, 05C35.

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Received 5 July 2001
Revised 4 March 2002