Cayley graphs of order kp are hamiltonian for k < 48

Abstract

We provide a computer-assisted proof that if G is any finite group of order kp, where 1 ≤ 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  ≤ 2).