Edge-transitive maps of low genus - Orbanić, Alen (Ars mathematica contemporanea, 2011)
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 classi?ed in the paper.
Keywords: edge-transitive map; edge-transitive tessellation; grafi simetrijskih tipov; graph theory; map on surface; povezavno tranzitivna tlakovanja; povezavno tranzitivni zemljevidi; symmetry type graph; teorija grafov; zemljevidi na ploskvah