Geodesic
Regular embeddings of cycles with multiple edges revisited
Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 177-194.

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Regular embeddings of cycles with multiple edges have been reappearing in the literature for quite some time, both in and outside topological graph theory. The present paper aims to draw a complete picture of these maps by providing a detailed description, classification, and enumeration of regular embeddings of cycles with multiple edges on both orientable and non-orientable surfaces. Most of the results have been known in one form or another, but here they are presented from a unique viewpoint based on finite group theory. Our approach brings additional information about both the maps and their automorphism groups, and also gives extra insight into their relationships.
DOI : 10.26493/1855-3974.626.f9d
Keywords: Regular embedding, multiple edge, Holder’s Theorem, Mobius map. 
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Kan Hu; Roman Nedela; Martin Škoviera; Naer Wang. Regular embeddings of cycles with multiple edges revisited. Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 177-194. doi : 10.26493/1855-3974.626.f9d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.626.f9d/

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