On the maximal cliques of the quadratic forms graph in even characteristic (Q753831)

Let V denote an n-dimensional vector space over the field of q elements. Associated with V is graph Quad (n,q), the vertices of which are the quadratic forms on V, with two forms adjacent if the rank of their difference is 1 or 2. The main result is that if m is a maximal clique of Quad (n,q) with q even, \(q>3\) such that \(| M| \geq \max \{q+4,9\}\), then M is either grand, cubic, quadratic or linear and moreover, grand, cubic, quadratic and linear cliques are maximal.