Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs associated with orthogonal collections of k-planes over finite
  fields   We study graphs coming from quadratic spaces over finite fields via
orthogonality which generalize a recent result given by Bishnoi, Ihringer, and
Pepe (2019). More precisely, we study the graph $\Gamma^{\square}(n,k,q)$ as
follows: the vertex set is the set of $k$-dimensional quadratic subspaces of a
fixed Lorentzian quadratic space
$(\mathbb{F}_{q}^{n},x_{1}^{2}+\cdots+x_{n-1}^{2}+\lambda x_{n}^{2})$ which are
isometrically isomorphic to $x_{1}^{2}+\cdots+x_{k}^{2}$. Here $\lambda$ is a
nonsquare in $\mathbb{F}_{q}$, and two vertices $x,y$ are adjacent if $x
\subseteq y^{\perp}$.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ