Note on cubic symmetric graphs of order 2p n

Let p be a prime and n a positive integer. In [J. Austral. Math. Soc. 81 (2006), 153–164], Feng and Kwak showed that if p>5thenevery connected cubic symmetric graph of order 2pn is a Cayley graph. Clearly, this is not true for p = 5 because the Petersen graph is non-Cayley. But they conjectured that this is true for p = 3. This conjecture is confirmed in this paper. Also, for the case when p = 2, we prove a slightly more general result, that is, every connected cubic vertex-transitive graph of order a power of 2 is a Cayley graph.