An infinite family of semisymmetric graphs constructed from affine geometries

A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. In this paper, using the affine geometries, we construct an infinite family X(p,n) of semisymmetric graphs of order 2pn and valency p, where p is a prime and p≥n≥3. Moreover, the graph X(3,3) is isomorphic to the Gray graph found in 1932.