It has been shown that there is a Hamilton cycle in every connected Cayley graph on each group G whose commutator subgroup is cyclic of prime-power order. This paper considers connected, vertex-transitive graphs X of order at least 3 where the automorphism group of X contains a transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs, only the Petersen graph is not Hamiltonian. © 1998 Elsevier Science B.V. All rights reserved.
Dobson, E., Gavlas, H., Morris, J., & Witte, D. (1998). Automorphism groups with cyclic commutator subgroup and Hamilton cycles. Discrete Mathematics, 189(1–3), 69–78. https://doi.org/10.1016/S0012-365X(98)00003-X