Regular balanced Cayley maps on ${\rm PSL}(2,p)$

TL;DR

This paper classifies regular balanced Cayley maps on the group PSL(2,p) for all primes p > 3, expanding the understanding of symmetric embeddings of Cayley graphs on this important family of groups.

Contribution

It provides a complete classification of RBCMs on PSL(2,p), a significant step beyond previous classifications on simpler groups.

Findings

Classified RBCMs for PSL(2,p) for all primes p > 3

Extended the classification framework to a new class of groups

Enhanced understanding of symmetric Cayley graph embeddings

Abstract

A {\it regular balanced Cayley map} (RBCM for short) on a finite group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface, with some special symmetric property. People have classified RBCM's for cyclic, dihedral, generalized quaternion, dicyclic, and semi-dihedral groups. In this paper we classify RBCM's on the group ${\rm PSL}(2,p)$ for each prime number $p>3$.