Subconstituents of orthogonal graphs of characteristic 2

The subconstituents of the (singular) orthogonal graphs over finite fields of characteristic 2 are studied. After considering the actions of the orthogonal group on the graphs, their parameters are calculated. We show that the first subconstituent is strongly regular and that for all but the smallest cases, the second subconstituent is quasi-strongly regular and edge regular. The automorphism group of the second subconstituent is also determined.