On finite subnormal Cayley graphs

TL;DR

This paper introduces subnormal Cayley graphs, characterizes 2-arc transitive cases, and provides a method to construct half-symmetric Cayley graphs, advancing understanding of their structure and symmetry properties.

Contribution

It defines subnormal Cayley graphs, proves their structure in 2-arc transitive cases, and offers a generic construction method for half-symmetric Cayley graphs.

Findings

A subnormal 2-arc transitive Cayley graph is either normal or a cover of a complete bipartite graph.

Established a method for constructing half-symmetric Cayley graphs.

Enhanced understanding of symmetry and structure in Cayley graphs.

Abstract

In this paper we introduce and study a type of Cayley graph -- subnormal Cayley graph. We prove that a subnormal 2-arc transitive Cayley graph is a normal Cayley graph or a normal cover of a complete bipartite graph $K_{p^d,p^d}$ with $p$ prime. Then we obtain a generic method for constructing half-symmetric (namely edge transitive but not arc transitive) Cayley graphs.