Construction of an Automorphic Graph on 280 Vertices Using Finite Geometries

Abstract

Nowadays, much information about different classes of distance-regular graphs is available (see survey [2]). The majority of these graphs were constructed using classical geometries over finite fields. As a rule one obtains in this way an infinite series of graphs. The classification problem for distance-transitive graphs admitting a transitive representation of a linear group became realisable. In the resolution of this problem some serious difficulties are expected regarding sporadic representations, i.e. those which do not belong to an infinite series. The elimination of distance-regular graphs which are not distance-transitive is also a significant step in the solution of this problem. These observations stimulate an interest in searching for special constructions which give a simple and beautiful description of certain distance-transitive graphs. The necessity of such constructions also arises in the interpretation of graphs which were discovered by means of a computer.