The Number of Complete Maps on Surfaces

Details The Number of Complete Maps on Surfaces The Number of Complete Maps on Surfaces

2006-07-31

arxiv.org/abs/math/0607790v1

Mathematics

General Mathematics

21 pages with 2 figures

Scientific paper

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.

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