The Number of Complete Maps on Surfaces

2006/07/31 by Linfan Mao, Mao, Linfan, Yanpei Liu +3 · 1 citation
Computer Science · Mathematics · #05C10 #05C25 #05C30 #Cellular Automata and Applications #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #General Mathematics (math.GM) #Geometric and Algebraic Topology #math.CO #math.GM #msc:05C10 #msc:05C25 #msc:05C30

paper · pdf · doi:10.48550/arxiv.math/0607790

21 pages with 2 figures

arxiv created 2006/07/31 · openalex publication_date 2006/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on its vertices. Applying a scheme for enumerating maps on surfaces with a given underlying graph, the numbers of unrooted complete maps on orientable or non-orientable surfaces are obtained.

Cited by

• Automorphisms and Enumeration of Maps of Cayley Graph of a Finite Group

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