Cubic non-normal Cayley graphs of order

A Cayley graph Cay ( G , S ) on a group G is said to be normal if the right regular representation R ( G ) of G is normal in the full automorphism group of Cay ( G , S ) . In this paper all connected cubic non-normal Cayley graphs of order 4 p 2 are constructed explicitly for each odd prime p . It is shown that there are three infinite families of cubic non-normal Cayley graphs of order 4 p 2 with p odd prime. Note that a complete classification of cubic non-Cayley vertex-transitive graphs of order 4 p 2 was given in [K. Kutnar, D. Marus˘ic˘, C. Zhang, On cubic non-Cayley vertex-transitive graphs, J. Graph Theory 69 (2012) 77–95]. As a result, a classification of cubic vertex-transitive graphs of order 4 p 2 can be deduced.