A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime, by Malnic et al. (A. Malnic, D. Marusic and C.Q. Wang, Cubic edge-transitive graphs of order 2p 3 , Discrete Math 274 (2004), 187-198), there exists a unique cubic semisymmetric cubic graph of order 2p 3 and by Feng et al. (Y. Feng, M. Ghasemi, C. Wang, Cubic semisymmetric graphs of order 6p 3 , Discrete Math 310 (2010) 2345-2355) a cubic semisymmetric graph of order 6p 3 exists if and only if p − 1 is divisible by 3. In this paper we prove that every cubic edge-transitive graph of order 12p 3 is vertex-transitive and so there is no cubic semisymmetric graph of order 12p 3 .
