Geodesic
Edge-transitive maps of low genus
Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 385-402.

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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.
DOI : 10.26493/1855-3974.249.3a6
Keywords: Edge-transitive map, edge-transitive tessellation, map on surface, symmetry type graph 
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Alen Orbanić; Daniel Pellicer; Tomaž Pisanski; Thomas W. Tucker. Edge-transitive maps of low genus. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 385-402. doi : 10.26493/1855-3974.249.3a6. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.249.3a6/

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