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

Abstract

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