# Splitting groups with cubic Cayley graphs of connectivity two

## TL;DR

This paper classifies all infinite groups with cubic Cayley graphs of connectivity two by analyzing their splittings over subgroups using Bass-Serre theory.

## Contribution

It provides a complete classification of infinite groups with specific Cayley graph properties based on group splittings.

## Key findings

- Classification of all infinite groups with cubic Cayley graphs of connectivity two
- Connection between Cayley graph connectivity and group splittings
- Application of Bass-Serre theory to group graph structures

## Abstract

A group $G$ splits over a subgroup $C$ if $G$ is either a free product with amalgamation $A \underset{C}{\ast} B$ or an HNN-extension $G=A \underset{C}{\ast} (t)$. We invoke Bass-Serre theory and classify all infinite groups which admit cubic Cayley graphs of connectivity two in terms of splittings over a subgroup.