# Classification of Cayley Rose Window Graphs

## TL;DR

This paper classifies Cayley rose window graphs, a specific family of symmetric tetravalent graphs, expanding the understanding of their algebraic and combinatorial properties.

## Contribution

It provides the first classification of Cayley rose window graphs, a subclass not previously characterized in the literature.

## Key findings

- Cayley rose window graphs are fully classified.
- New structural properties of Cayley rose window graphs are identified.
- Connections to existing classifications of symmetric graphs are established.

## Abstract

Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edge-transitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.