# Regular $t$-balanced Cayley maps on split metacyclic $2$-groups

## TL;DR

This paper classifies all regular t-balanced Cayley maps on a specific class of split metacyclic 2-groups, advancing understanding of symmetric embeddings of Cayley graphs on these groups.

## Contribution

It provides a complete classification of regular t-balanced Cayley maps for split metacyclic 2-groups, a previously uncharacterized class.

## Key findings

- Complete classification achieved for the specified groups.
- Identification of conditions for the existence of such Cayley maps.
- Enhanced understanding of symmetric embeddings on split metacyclic 2-groups.

## Abstract

A regular $t$-balanced Cayley map on a group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface with certain special symmetric properties. We completely classify regular $t$-balanced Cayley maps for a class of split metacyclic $2$-groups.