Automorphism groups with cyclic commutator subgroup and Hamilton cycles

1997/02/04 by Dobson, Edward, Gavlas, Heather, Morris, Joy +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9702226

Abstract

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.

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