Automorphism groups with cyclic commutator subgroup and Hamilton cycles

It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-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.

• Type: Journal
• Year: 1998
• Where: DM
• Authors: Edward Dobson, Heather Gavlas, Joy Morris, Dave Witte
• Keywords: Commutator Subgroup, Connected Cayley Graph, DM 1998, Prime-power Order