On Bi-rotary Maps of Negative Prime Power Euler Characteristic

2025/09/16 by Jiyong Chen, Chen, Jiyong, Cai Heng Li +2
Mathematics · #Advanced Topics in Algebra #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2509.12687

Abstract

A map is bi-orientable if it admits an assignment of local orientations to its vertices such that for every edge, the local orientations at its two endpoints are opposite. Such an assignment is called a bi-orientation of the map. A bi-orientable map is bi-rotary if its automorphism group contains an arc-regular subgroup that preserves the bi-orientation. In this paper, we characterize the automorphism group structure of bi-rotary maps whose Euler characteristic is a negative prime power.

Citations

• Arc-transitive maps with edge number coprime to the Euler characteristic -- I
• Orientably-regular embeddings of complete multigraphs
• Locally Finite Vertex-Rotary Maps and Coset Graphs with Finite Valency and Finite Edge Multiplicity
• Automorphism groups of edge-transitive maps

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