# Edge-transitive embeddings of complete graphs

## TL;DR

This paper completes the classification of edge-transitive embeddings of complete graphs by building on previous work and utilizing the Graver-Watkins classification of edge-transitive maps.

## Contribution

It provides a comprehensive classification of all edge-transitive embeddings of complete graphs, extending earlier partial results.

## Key findings

- Complete classification of edge-transitive embeddings achieved.
- Utilized Graver-Watkins classification of edge-transitive maps.
- Extended previous work by Biggs, James, Wilson, and the author.

## Abstract

Building on earlier work of Biggs, James, Wilson and the author, and using the Graver-Watkins description of the 14 classes of edge-transitive maps, we complete the classification of the edge-transitive embeddings of complete graphs.