2006/07/31 by Linfan Mao, Mao, Linfan, Yanpei Liu +1
Computer Science · Engineering · Mathematics · #05C10 #05C25 #05C30 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #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/0607791
17 pages with 1 figure
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
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≅ G× 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.