Normal edge-transitive Cayley graphs of Frobenius groups

B.P. Corr; Cheryl Praeger

doi:10.1007/s10801-015-0603-4

Normal edge-transitive Cayley graphs of Frobenius groups

B.P. Corr, Cheryl Praeger

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York. 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 $${{\mathrm{Sym}}}(G)$$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.

Original language	English
Pages (from-to)	803-827
Journal	Journal of Algebraic Combinatorics
Volume	42
Issue number	3
DOIs	https://doi.org/10.1007/s10801-015-0603-4
Publication status	Published - 2015

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AB - © 2015, Springer Science+Business Media New York. 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 $${{\mathrm{Sym}}}(G)$$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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Normal edge-transitive Cayley graphs of Frobenius groups

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