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

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

2006-07-31

arxiv.org/abs/math/0607791v1

Mathematics

General Mathematics

17 pages with 1 figure

Scientific paper

A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. In this paper, applying Tutte's algebraic representation of map, new ideas for enumerating non-equivalent orientable or non-orientable maps of graph are presented. By determining automorphisms of maps of Cayley graph $\Gamma={\rm Cay}(G:S)$ with ${\rm Aut} \Gamma\cong G\times H$ on locally, orientable and non-orientable surfaces, formulae for the number of non-equivalent maps of $\Gamma$ on surfaces (orientable, non-orientable or locally orientable) are obtained . Meanwhile, using reseults on GRR graph for finite groups, we enumerate the non-equivalent maps of GRR graph of symmetric groups, groups generated by 3 involutions and abelian groups on orientable or non-orientable surfaces.

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