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The Number of Complete Maps on Surfaces

Linfan Mao·Yanpei Liu·Feng Tian
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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.

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Linfan Mao, Yanpei Liu, Feng Tian. 2006-07-31. The Number of Complete Maps on Surfaces. https://arxiv.org/abs/math/0607790

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