Automorphisms of cubic Cayley graphs of order

In this paper the automorphism groups of connected cubic Cayley graphs of order 2 p q for distinct odd primes p and q are determined. As an application, all connected cubic non-symmetric Cayley graphs of order 2 p q are classified and this, together with classifications of connected cubic symmetric graphs and vertex-transitive non-Cayley graphs of order 2 p q given by the last two authors, completes a classification of connected cubic vertex-transitive graphs of order 2 p q .