Graphs associated with orthogonal collections of k-planes over finite fields

We study graphs coming from quadratic spaces over finite fields which generalize a recent result given by Bishnoi, Ihringer, and Pepe (2020). More precisely, we the graph Γ□(n,k,q) defined as follows: vertex set is of k-dimensional subspaces fixed space (Fqn,x12+⋯+xn−12+λxn2) isometrically isomorphic to x12+⋯+xk2. Here λ non-square in Fq, two vertices x,y are adjacent if x⊆y⊥.