Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian

TL;DR

This paper proves that all connected Cayley graphs on finite nilpotent groups with cyclic commutator subgroup contain a Hamiltonian cycle, extending understanding of Hamiltonian properties in algebraic graph theory.

Contribution

It establishes that every connected Cayley graph on such groups is Hamiltonian, a new result in the study of Cayley graphs of nilpotent groups.

Findings

All connected Cayley graphs on these groups have Hamiltonian cycles.

The result applies to any finite nilpotent group with cyclic commutator subgroup.

This extends previous work on Hamiltonian cycles in Cayley graphs.

Abstract

We show that if G is any nilpotent, finite group, and the commutator subgroup of G is cyclic, then every connected Cayley graph on G has a hamiltonian cycle.