Connected Cayley graphs of semi-direct products of cyclic groups of prime order by abelian groups are hamiltonian

Abstract

In this paper it is shown that every connected Cayley graph of a semi-direct product of a cyclic group of prime order by an abelian group is hamiltonian. In particular, every connected Cayley graph of a group G is hamiltonian provided that G is of order greater than 2 and it contains a normal cyclic subgroup N of prime order such that the quotient group G/ N is abelian and its order is relatively prime to that of N.