# On edge-primitive graphs with soluble edge-stabilizers

## TL;DR

This paper classifies edge-primitive, 2-arc-transitive graphs with soluble edge-stabilizers, advancing understanding of their symmetry properties and automorphism groups.

## Contribution

It provides a complete classification of a specific class of highly symmetric graphs with soluble edge-stabilizers.

## Key findings

- Classification of edge-primitive, 2-arc-transitive graphs with soluble edge-stabilizers
- Identification of automorphism group actions on these graphs
- Characterization of their symmetry and structural properties

## Abstract

A graph is edge-primitive if its automorphism group acts primitively on the edge set, and 2-arc-transitive if its automorphism group acts transitively on the set of 2-arcs. In this paper, we present a classification for those edge-primitive graphs which are 2-arc-transitive and have soluble edge-stabilizers.