Cubic semisymmetric graphs of order $ 40p $

A simple graph $\Gamma$ is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. A simple graph $\Gamma$ is called cubic whenever it is $ 3 $-regular. An important research problem is the classification of semisymmetric cubic graphs of different orders. The purpose of this article is the classification of semisymmetric cubic graphs of order $ 40p $, where p is a prime number. We show that for $ p\ne3,31 $ such a graph Does not exist. Suppose p is a prime number, Folkman showed in\cite{fo} that there is no semisymmetric graph of order $ 2p $ or $ 2p^2 $. We show that if $\Gamma$ is a semisymmetric cubic graph of order $ 40p $, then $ p=3 $ and $\Gamma$ is isomorphic to a semisymmetric cubic graph of order $ 120 $ or $ p=31 $ and $\Gamma$ is isomorphic to the coset graph $ C(L_2 (31):\mathbb{S}_4,\mathbb{S}_4).$ Our basic tools in this research are automorphism of graphs, simple groups, solevable groups and permutation groups.