Some Hamiltonian Cayley Graphs

Abstract

No negative example or positive proof is known for the conjecture that every Cayley graph is hamiltonian. Trivalent Cayley graphs are especially interesting, being at the same time the simplest nontrivial Cayley graphs and those most likely to be nonhamiltonian, because of the small number of edges. In this note, we use the eulerian or hamiltonian structure of one graph to find a hamiltonian cycle in another. This technique is then used to expand certain trivalent Cayley graphs into hamiltonian Cayley graphs at the expense of higher valency.