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

Linfan Mao; Yanpei Liu

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

Linfan Mao·Yanpei Liu

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Abstract

A map is a connected topological graph $Γ$ 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 $Γ={\rm Cay}(G:S)$ with ${\rm Aut} Γ\cong G\times H$ on locally, orientable and non-orientable surfaces, formulae for the number of non-equivalent maps of $Γ$ 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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Linfan Mao, Yanpei Liu. 2006-07-31. Automorphisms and Enumeration of Maps of Cayley Graph of a Finite Group. https://arxiv.org/abs/math/0607791

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