Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian

TL;DR

This paper proves that for certain finite groups with a cyclic commutator subgroup of order pq, all connected Cayley graphs on these groups contain a Hamiltonian cycle, extending understanding of Hamiltonian properties in Cayley graphs.

Contribution

It establishes that all connected Cayley graphs on finite odd-order groups with a cyclic commutator subgroup of order pq are Hamiltonian, a new result in algebraic graph theory.

Findings

All connected Cayley graphs on specified groups have Hamiltonian cycles.

The result applies to groups with cyclic commutator subgroup of order pq.

It extends previous work on Hamiltonian cycles in Cayley graphs.

Abstract

We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamiltonian cycle.