On hamiltonian cycles in Cayley graphs of order pqrs

TL;DR

This paper proves that all connected Cayley graphs of groups with order equal to the product of four distinct odd primes contain a Hamiltonian cycle, extending understanding of Hamiltonian properties in Cayley graphs.

Contribution

It establishes that for groups of order pqrs with distinct odd primes, every connected Cayley graph has a Hamiltonian cycle, a new result in algebraic graph theory.

Findings

All connected Cayley graphs of groups of order pqrs have Hamiltonian cycles.

The result applies to groups with four distinct odd prime factors.

Supports conjectures about Hamiltonian cycles in Cayley graphs of finite groups.

Abstract

Let $G$ be a finite group. We show that if $|G| = pqrs$, where $p$, $q$, $r$, and $s$ are distinct odd primes, then every connected Cayley graph on $G$ has a hamiltonian cycle.