The planar cubic Cayley graphs of connectivity 2

TL;DR

This paper classifies all planar cubic Cayley graphs with connectivity 2, providing explicit presentations and embeddings, thereby completing the description of all such graphs.

Contribution

It offers a complete classification and explicit constructions for planar cubic Cayley graphs of connectivity 2, extending previous work to cover all cases.

Findings

Explicit presentations for each graph

Complete classification of planar cubic Cayley graphs

Explicit embeddings provided

Abstract

We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.