The 4-Regular Edge-Transitive Graphs of Girth 4

TL;DR

This paper characterizes all 4-regular, edge-transitive graphs with girth four, identifying four infinite families and four exceptional graphs, thus providing a complete classification of this specific graph class.

Contribution

It provides a complete classification of 4-regular, edge-transitive graphs with girth four, including infinite families and exceptional cases, filling a gap in graph theory.

Findings

Identified four infinite families of graphs.

Discovered four exceptional graphs.

Provided a complete classification of the class.

Abstract

This paper presents a characterization of edge-transitive graphs which are four regular and have girth four. This class consists of four infinite families plus four exceptional graphs.