Edge-transitive maps of low genus

Alen Orbanić, Daniel Pellicer, Tomaž Pisanski, Thomas W. Tucker

Abstract


Graver and Watkins classified edge-transitive maps on closed surfaces into fourteen types. In this note we study these types for maps in orientable and non-orientable surfaces of small genus, including the Euclidean and hyperbolic plane. We revisit both finite and infinite one-ended edge-transitive maps. For the finite ones we give precise description that should enable their enumeration for a given number of edges. Edge-transitive maps on surfaces with small genera are classified in the paper.

Keywords


Edge-transitive map, edge-transitive tessellation, map on surface, symmetry type graph

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DOI: https://doi.org/10.26493/1855-3974.249.3a6

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