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arXiv · 1401.1883

Normal Edge-Transitive Cayley Graphs of Frobenius Groups

Brian P. Corr·Cheryl E. Praeger
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Abstract

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 $\operatorname{Sym}(G)$). 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.

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Brian P. Corr, Cheryl E. Praeger. 2014-01-09. Normal Edge-Transitive Cayley Graphs of Frobenius Groups. https://arxiv.org/abs/1401.1883

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