# Cayley graphs on groups with commutator subgroup of order 2p are hamiltonian

## TL;DR

This paper proves that for finite groups with a specific commutator subgroup order, all connected Cayley graphs on these groups contain Hamiltonian cycles, expanding understanding of Hamiltonian properties in algebraic graph theory.

## Contribution

It establishes that all connected Cayley graphs on groups with a commutator subgroup of order 2p (p odd prime) are Hamiltonian, a new result in algebraic graph theory.

## Key findings

- All connected Cayley graphs on such groups are Hamiltonian.
- The result applies to groups with commutator subgroup order 2p, p odd prime.
- This advances the classification of Hamiltonian Cayley graphs.

## Abstract

We show that if G is a finite group whose commutator subgroup [G,G] has order 2p, where p is an odd prime, then every connected Cayley graph on G has a hamiltonian cycle.