Geodesic
Normal edge-transitive Cayley graphs of Frobenius groups
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 803-827.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

A Cayley graph for a group $G$ is called normal edge-transitive if it admits an edge-transitive action of some subgroup of the holomorph of $G$ [the normaliser of a regular copy of $G$ in $\mathrm{Sym}(G)]$. 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.
Classification : 05C25, 20D10
Keywords: Cayley graphs, group theory, algebraic graph theory, Frobenius groups 
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     author = {Corr, Brian P. and Praeger, Cheryl E.},
     title = {Normal edge-transitive {Cayley} graphs of {Frobenius} groups},
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Corr, Brian P.; Praeger, Cheryl E. Normal edge-transitive Cayley graphs of Frobenius groups. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 803-827. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a4/