AI 中文总结
本文对二次型各向同性关联方案中定义Deza图的非平凡关系并集进行分类，除已知相切族外，发现4个特殊Deza图并确定其谱、子图及几何或群论描述。
AI 中文摘要
设$Q^\varepsilon(3,q)$，其中$\varepsilon\in\{+,-\}$且$q>3$为奇数，是射影平面$PG(3,q)$上非退化的双曲或椭圆二次型。固定两类各向同性点中的一类，由于该类中两个不同点的连线与二次型相切、相交或外离，可得到一个3类关联方案。本文对其所有非平凡关系并集（即Deza图）进行分类，除已知的相切族外，恰好出现4个特殊严格Deza图，参数分别为$(360,135,54,45)$、$(369,108,36,27)$、$(65,34,18,15)$和$(168,111,75,70)$；本文确定了它们的谱和Deza子图，并给出这4个特殊图的几何或群论描述。
英文摘要
Let $Q^\varepsilon(3,q)$, where $\varepsilon\in\{+,-\}$ and $q>3$ is odd, be a non-degenerate hyperbolic or elliptic quadric of $PG(3,q)$. Fix one of the two quadratic classes of anisotropic points. Since the line joining two distinct points of this class is tangent, secant, or external to the quadric, one obtains a $3$-class association scheme. We classify all non-trivial unions of its relations which define Deza graphs. In addition to the previously known tangency family, exactly four exceptional strictly Deza graphs occur, with parameters $(360,135,54,45)$, $(369,108,36,27)$, $(65,34,18,15)$ and $(168,111,75,70)$. We determine their spectra and Deza children and give geometric or group-theoretic descriptions of all four exceptional graphs.
