Edge-transitive maps of low genus

Authors

  • Alen Orbanić University of Ljubljana
  • Daniel Pellicer Instituto de Matemáticas, Universidad Nacional Autónoma de México
  • Tomaž Pisanski University of Ljubljana
  • Thomas W. Tucker Colgate University

DOI:

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

Keywords:

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

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.

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Published

2011-10-22

Issue

Vol. 4 No. 2 (2011)

Section

GEMS 2009 - Tale, Slovakia

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/