Regular embeddings of cycles with multiple edges revisited

Kan Hu, Roman Nedela, Martin Škoviera, Naer Wang

Abstract


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.


Keywords


Regular embedding, multiple edge, Holder’s Theorem, Mobius map.

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DOI: https://doi.org/10.26493/1855-3974.626.f9d

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications