Cayley graphs of order kp are hamiltonian for k < 48

TL;DR

This paper proves that all connected Cayley graphs of groups with order kp (k<48, p prime) are Hamiltonian, except for the trivial case, using a computer-assisted approach.

Contribution

It provides a comprehensive computer-assisted proof that all such Cayley graphs are Hamiltonian, extending known results to a broader class of group orders.

Findings

All connected Cayley graphs of order less than 48 are either Hamiltonian connected or Hamiltonian laceable.

The proof confirms Hamiltonian properties for groups of order kp with k<48 and p prime.

The exception is the trivial case where kp=2.

Abstract

We provide a computer-assisted proof that if G is any finite group of order kp, where k < 48 and p is prime, then every connected Cayley graph on G is hamiltonian (unless kp = 2). As part of the proof, it is verified that every connected Cayley graph of order less than 48 is either hamiltonian connected or hamiltonian laceable (or has valence less than three).