On the automorphisms of a family of small q-regular graphs of girth 8

In this paper we investigate the automorphisms of a family small (q,8)-graphs order 2q3 − 2q which are obtained as induced subgraphs incidence graph classical generalized quadrangle q. We show that for q an odd prime power, automorphism group has four orbits on set vertices, thus investigated graphs cannot be Cayley or lifts dipole.