A classification of vertex-reversing maps with Euler characteristic coprime to the edge number

2025/10/08 by Cai Heng Li, Luyi Liu, Li, Cai Heng +4 · 1 citation
Mathematics · #05C25 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:05C25 #msc:20D10 #msc:20D20

paper · pdf · doi:10.48550/arxiv.2510.07033

openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/30 · arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

An arc-regular map is vertex-reversing if the automorphism group has dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose Euler characteristic is coprime to the edge number. The classification establishes that such maps fall into four families: \D_2n-maps, (\D_2m×\D_2n)-maps, (\ZZ_mnℓ:\D₄)-maps, and (\ZZ_{3^f n}.§₄)-maps, with the parameters specified in the main theorem. Moreover, for each family, we provide an explicit formula for the Euler characteristic.

Citations

• Locally Finite Vertex-Rotary Maps and Coset Graphs with Finite Valency and Finite Edge Multiplicity
• Automorphism groups of edge-transitive maps

Cited by

• Finite groups and arc-transitive maps of square-free Euler characteristic

Related

• Arc-transitive maps with coprime Euler characteristic and edge number -- II
• Arc-transitive maps with edge number coprime to the Euler characteristic -- I
• Automorphism groups of edge-transitive maps
• Vertex-transitive maps with Schläfli type 3, 7
• Finite simple automorphism groups of edge-transitive maps