Cayley graphs of order 16p are hamiltonian

TL;DR

This paper proves that for any finite group G of order 16p, with p prime, every Cayley graph generated by any set S contains a Hamiltonian cycle, confirming Hamiltonicity in these graphs.

Contribution

It establishes that all Cayley graphs of groups of order 16p are Hamiltonian, regardless of the generating set, extending known results to this class of groups.

Findings

All Cayley graphs of order 16p are Hamiltonian.

Hamiltonian cycles exist for any generating set in these graphs.

The result applies to groups of order 16p for any prime p.

Abstract

Suppose G is a finite group, such that |G| = 16p, 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).