Classification of edge-transitive propeller graphs

TL;DR

This paper introduces a new family of tetravalent graphs called propeller graphs, classifies all arc-transitive instances into four subfamilies, and discusses open questions and conjectures for future research.

Contribution

The paper defines propeller graphs and completely classifies all arc-transitive examples into four specific subfamilies, advancing understanding of their symmetry properties.

Findings

All arc-transitive propeller graphs belong to four subfamilies.

The paper provides explicit constructions for these subfamilies.

Open questions and conjectures are proposed for future work.

Abstract

In this paper, we introduce a family of tetravalent graphs called propeller graphs, denoted by $Pr_{n}(b,c,d)$. We then produce three infinite subfamilies and one finite subfamily of arc-transitive propeller graphs, and show that all such graphs are necessarily members of one of these four subfamilies, up to isomorphism. We close the paper with questions for further investigation, as well as a few conjectures.