3 - Graphs related to polar spaces

Summary

In this chapter we discuss strongly regular graphs arising from non-degenerate reflexive forms on a finite vector space not isomorphic to the point-graphs. These comprise the graphs on non-singular or nonisotropic points with respect to reflexive forms over small fields, the half spin graphs with a discussion of triality, the rank 5 hyperbolic case, the graph on the maximal subspaces of rank 3 orthogonal and symplectic polar spaces, affine polar graphs including a detailed discussion of the affine half spin graphs, forms graphs, affine graphs with a Baer subspace or a hyperoval at infinity, and Grassmann graphs. In the last paragraph, we analyse the polar graphs arising from non-isotropic points with respect to various forms over the field of two elements and discuss the mutual relations via the local structure.