Cayley graphs of order 6pq are Hamiltonian

TL;DR

This paper proves that Cayley graphs of certain finite groups of order 6pq or 7pq, with p and q as distinct primes, always contain a Hamiltonian cycle, confirming a conjecture for these cases.

Contribution

It establishes the existence of Hamiltonian cycles in Cayley graphs of groups with orders 6pq and 7pq, expanding the classes of groups known to have Hamiltonian Cayley graphs.

Findings

Cayley graphs of order 6pq have Hamiltonian cycles.

Cayley graphs of order 7pq have Hamiltonian cycles.

Supports the conjecture that all Cayley graphs of finite groups are Hamiltonian.

Abstract

Assume G is a finite group, such that |G|= 6pq or 7pq, where p and q are distinct prime numbers, and let S be a generating set of G. We prove there is a Hamiltonian cycle in the corresponding Cayley graph Cay(G;S).