Edge-transitive maps of low genus
Keywords:Edge-transitive map, edge-transitive tessellation, map on surface, symmetry type graph
AbstractGraver 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.
GEMS 2009 - Tale, Slovakia
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