Classifying edge-biregular maps of negative prime Euler characteristic

TL;DR

This paper classifies all finite edge-biregular maps on surfaces with negative prime Euler characteristic, expanding understanding of symmetrical maps in topological graph theory.

Contribution

It provides a complete classification of edge-biregular maps on surfaces with negative prime Euler characteristic, a previously uncharted area.

Findings

All such maps are classified explicitly.

The classification is complete for surfaces with negative prime Euler characteristic.

The work links group actions to map symmetries.

Abstract

An edge-biregular map arises as a smooth normal quotient of a unique index-two subgroup of a full triangle group acting with two edge-orbits. We give a classification of all finite edge-biregular maps on surfaces of negative prime Euler characteristic.