Automorphism groups with cyclic commutator subgroup and Hamilton cycles

✍ Scribed by Edward Dobson; Heather Gavlas; Joy Morris; Dave Witte

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 670 KB
• Volume: 189
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(98)00003-x

✦ Synopsis

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.