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- ItemCaley graphs of order 16p are hamiltonian(Drustvo Matematikov, Fizikov in Astronomov, 2012) Curran, Stephen J.; Morris, Dave Witte; Morris, JoySuppose 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).
- ItemHamiltonian cycles in Caley graphs whose order has few prime factors(Drustvo Matematikov, Fizikov in Astronomov, 2012) Kutnar, Klavdija; Marusic, Dragan; Morris, Dave Witte; Morris, Joy; Sparl, PrimozWe prove that if Cay(G;S) is a connected Cayley graph with n vertices,and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with 24 6= k < 32, or of the form kpq with k ≤ 5,or of the form pqr,or of the form kp2 with k ≤ 4,or of the form kp3 with k ≤ 2.
- ItemOn colour-preserving automorphisms of Caley graphs(Drustvo Matematikov, Fizikov in Astronomov, 2016) Hujdurovic, Ademir; Kutnar, Klavdija; Morris, Dave Witte; Morris, JoyWe study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups G, such that every such automorphism of every connected Cayley graph on G has a very simple form: the composition of a left-translation and a group automorphism. We ﬁnd classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them.