Hamiltonicity in generalized quasi-dihedral groups

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.

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