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Normal edge-transitive Cayley graphs of Frobenius groups

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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 \({{\mathrm{Sym}}}(G)\)]. 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.

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Acknowledgments

The first author is supported by an Australian Mathematical Society Lift-Off Fellowship.

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Correspondence to Brian P. Corr.

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Corr, B.P., Praeger, C.E. Normal edge-transitive Cayley graphs of Frobenius groups. J Algebr Comb 42, 803–827 (2015). https://doi.org/10.1007/s10801-015-0603-4

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  • DOI: https://doi.org/10.1007/s10801-015-0603-4

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