Cayley graphs of order 27p are hamiltonian

TL;DR

This paper proves that for any finite group of order 27p, where p is prime, the Cayley graph generated by any set of generators always contains a Hamiltonian cycle.

Contribution

It establishes that Cayley graphs of groups with order 27p are Hamiltonian for any generating set, extending known results to this specific group order.

Findings

Cayley graphs of order 27p are Hamiltonian for any generating set

The result applies to all groups of this order, regardless of the generating set chosen

Supports conjectures about Hamiltonicity in Cayley graphs of finite groups

Abstract

Suppose G is a finite group, such that |G| = 27p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).