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 study the graph ${\mathrm{\Gamma }}^{\square }(n,k,q)$ defined as follows: the vertex set is the set of k-dimensional quadratic subspaces of a fixed quadratic space $({\mathbb{F}}_q^n,x_1^2+\cdots +x_{n-1}^2+\lambda x_n^2)$ isometrically isomorphic to $x_1^2+\cdots +x_k^2$. Here λ is a non-square in ${\mathbb{F}}_q$, and two vertices $x,y$ are adjacent if $x\subseteq y^{\perp }$.

中文翻译：

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与有限域上k平面正交集合相关​​的图

我们研究来自有限域上的二次空间的图，这些图概括了 Bishnoi、Ihringer 和 Pepe（2020）给出的最近结果。更准确地说，我们研究图形${\mathrm{\Gamma }}^{\square }(n,克,q)$定义如下：顶点集是一个固定二次空间的k维二次子空间的集合$({\mathbb{F}}_q^n,X_1^2+\cdots +X_{n-1}^2+\lambda X_n^2)$ 等距同构 $X_1^2+\cdots +X_{克}^2$. 这里λ是一个非平方${\mathbb{F}}_q$, 和两个顶点 $X,是$ 相邻，如果 $X\subseteq {是}^{\perp }$.