Chapter

Topics in Discrete Mathematics

Volume 26 of the series Algorithms and Combinatorics pp 591-609

Regular Maps on a Given Surface: A Survey

  • Jozef ŠiráňAffiliated withDepartment of Mathematics, SvF, Slovak University of TechnologyDepartment of Mathematics, University of Auckland

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Abstract

Regular maps are cellular decompositions of closed surfaces with the highest ‘level of symmetry’, meaning that the automorphism group of the map acts regularly on flags. We survey the state-of-the-art of the problem of classification of regular maps on a given surface and outline directions of future research in this area.

Keywords

Graph surface embedding map automorphism regular map