Tetravalent edge-transitive Cayley graphs of Frobenius groups

TL;DR

This paper characterizes a class of highly symmetric Cayley graphs of Frobenius groups, introduces methods for their construction, and presents a new family of half-transitive graphs with specific symmetry properties.

Contribution

It provides a new characterization and construction methods for edge-transitive Cayley graphs of Frobenius groups, and introduces a novel family of half-transitive graphs.

Findings

Characterization of a class of edge-transitive Cayley graphs

Construction methods for Cayley graphs with symmetry

Introduction of a new family of half-transitive graphs

Abstract

In this paper, we give a characterization for a class of edge-transitive Cayley graphs, and provide methods for constructing Cayley graphs with certain symmetry properties. Also this study leads to construct and characterise a new family of half-transitive graphs.