Quasi-vertex-transitive maps on the plane

2019/09/30 by Arun Maiti
Mathematics · #Algebraic Geometry and Number Theory #Automorphism #Automorphism group #Combinatorics #Discrete mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Graph #Homogeneous #Mathematics #Transitive relation #Vertex (graph theory) #math.CO #math.GT

paper · pdf · doi:10.1016/j.disc.2020.111911

published as Discrete Math. 343 (2020), no. 7 · 8 pages, 8 figures

arxiv created 2020/03/23 · openalex publication_date 2020/03/23 · arxiv updated 2020/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types [p³, 3] for p ≡ 1 (mod 6), but there doesn't exist vertex-transitive map of such types. In particular, we determine the surface with the lowest possible genus that admit a polyhedral map of type [5³, 3].

Citations

• An enduring error
• Tilings and Patterns.
• Subgroups of Surface Groups are Almost Geometric