Cubic vertex-transitive graphs on up to 1280 vertices

TL;DR

This paper combines theoretical insights and computational methods to classify all cubic vertex-transitive graphs up to 1280 vertices and all tetravalent arc-transitive graphs up to 640 vertices, expanding understanding of symmetric graph structures.

Contribution

It provides a complete classification of cubic vertex-transitive graphs up to 1280 vertices and tetravalent arc-transitive graphs up to 640 vertices, using new theoretical results and computer calculations.

Findings

Complete list of cubic vertex-transitive graphs up to 1280 vertices.

Complete list of tetravalent arc-transitive graphs up to 640 vertices.

New theoretical results on graph symmetry properties.

Abstract

A graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arc- set, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. In the process, we also construct all tetravalent arc-transitive graphs of order at most 640.