English

Normal Edge-Transitive Cayley Graphs of Frobenius Groups

Combinatorics 2014-01-10 v1 Group Theory

Abstract

A Cayley Graph for a group GG is called normal edge-transitive if it admits an edge-transitive action of some subgroup of the Holomorph of GG (the normaliser of a regular copy of GG in Sym(G)\operatorname{Sym}(G)). We complete the classification of normal edge-transitive Cayley graphs of order a product of two primes by dealing with Cayley graphs for Frobenius groups of such orders. We determine the automorphism groups of these graphs, proving in particular that there is a unique vertex-primitive example, namely the flag graph of the Fano plane.

Keywords

Cite

@article{arxiv.1401.1883,
  title  = {Normal Edge-Transitive Cayley Graphs of Frobenius Groups},
  author = {Brian P. Corr and Cheryl E. Praeger},
  journal= {arXiv preprint arXiv:1401.1883},
  year   = {2014}
}