On edge-hamiltonian Cayley graphs (Q1329801)

The authoress extends a result of Alspach and Zhang regarding the hamiltonicity of every Cayley graph on a dihedral group. She shows that a cubic Cayley graph on a dihedral group with minimal generating set \(\{h_ i,h_ jh_ k,h_ l\}\) of order-2 elements, such that \(h_ i\), \(h_ j\), \(h_ k\) are reflections and \(h_ ih_ j\) is of prime order, is hamiltonian. She proves too that if a Cayley graph on a dihedral group is hamiltonian, it must be edge-hamiltonian.