Abstract
We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p, where p is a prime number. As a consequence we prove if |G| = 2δ p, δ = 0, 1,2 and p prime, then Λ = Cay(G, S) is a connected normal \(\tfrac{1} {2}\) arc-transitive Cayley graph only if G = F 4p , where S is an inverse closed generating subset of G which does not contain the identity element of G and F 4p is a group with presentation \(F_{4p} = \left\langle {\left. {a,b} \right|a^p = b^4 = 1,b^{ - 1} ab = a^\lambda } \right\rangle\), where λ 2 ≠ −1 (mod p).
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Darafsheh, M.R., Assari, A. Normal edge-transitive Cayley graphs on non-abelian groups of order 4p, where p is a prime number. Sci. China Math. 56, 213–219 (2013). https://doi.org/10.1007/s11425-012-4415-x
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DOI: https://doi.org/10.1007/s11425-012-4415-x