Hamiltonicity in generalized quasi-dihedral groups

Abstract

Witte Morris showed in [21] that every connected Cayley graph of a finite (generalized) dihedral group has a Hamiltonian path. The infinite dihedral group is defined as the free product with amalgamation ${\mathbb{Z}}_2\ast {\mathbb{Z}}_2$. We show that every connected Cayley graph of the infinite dihedral group has both a Hamiltonian double ray, and extend this result to all two-ended generalized quasi-dihedral groups.