The last subconstituent of the Hemmeter graph

We prove that when q is any odd prime power, the distance-2 graph on the set of vertices at maximal distance D from any fixed vertex of the Hemmeter graph Hem D(q) is isomorphic to the graph Quad(D-1)(q) of quadratic forms on F-q(D-1). (c) 2007 Elsevier B.V. All rights reserved.