Cayley graphs of order 27p are hamiltonian

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).Comment: 13 pages, no figures; minor revisions, including suggestions from a referee; this version is to appear in the International Journal of Combinatoric

Cayley graphs of order kp are hamiltonian for k < 48

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).Comment: 16 pages. GAP source code is available in the ancillary file

Cayley graphs of order 30p are Hamiltonian

Suppose G is a finite group, such that |G|=30p, 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). © 2012 Elsevier B.V. All rights reserved

Cayley graphs of order 6pq are Hamiltonian

Assume G is a finite group, such that |G| is either 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 on G with connecting set S