论文标题
与有限字段的K-plans的正交集合相关的图形
Graphs associated with orthogonal collections of k-planes over finite fields
论文作者
论文摘要
我们通过正交性研究了来自有限场上的二次空间的图形，这概括了Bishnoi，Ihringer和Pepe（2019）给出的最新结果。更确切地说，我们研究图$γ^{\ square}（n，k，q）$，如下所示：顶点集是固定lorentzian Quadratic Space的$ k $二维二次二次子空间$） $ x_ {1}^{2}+\ cdots+x_ {k}^{2} $。这里$λ$是$ \ mathbb {f} _ {q} $中的非Quare，如果$ x \ subseteq y^{\ perp} $，则两个vertices $ x，y $相邻。
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 $Γ^{\square}(n,k,q)$ as follows: the vertex set is the set of $k$-dimensional quadratic subspaces of a fixed Lorentzian quadratic space $(\mathbb{F}_{q}^{n},x_{1}^{2}+\cdots+x_{n-1}^{2}+λx_{n}^{2})$ which are isometrically isomorphic to $x_{1}^{2}+\cdots+x_{k}^{2}$. Here $λ$ is a nonsquare in $\mathbb{F}_{q}$, and two vertices $x,y$ are adjacent if $x \subseteq y^{\perp}$.
