发表机构
Suzhou University of Technology; North China University of Technology（苏州科技大学; 华北理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究偶特征正交图第一子构成的结构，证明其为仿射极图补图，确定其自同构群、独立数、色数、最大团及核，并给出二元情形三重传递性的简短证明。
AI 中文摘要
在偶特征下，正交图在奇异点处的第一子构成被证明是仿射极图的补图。这一识别给出了作为仿射半相似群的全自同构群，并提供了到环境图的显式扩展。最大独立集是极大全奇异子空间的仿射陪集，由此得到独立数和色数。在加型中，Delsarte 团与通过基点的卵形线一一对应，从而得出一个尖锐的秩阈值。在 $\mathbb{F}_2$ 上，我们确定了每个维数下的精确最大团数，证明了所有最大团构成单个轨道，并获得了每个第一子构成的核。一个统一的 Witt 延拓论证给出了二元局部图三重传递性的简短证明。
英文摘要
In even characteristic, the first subconstituent of an orthogonal graph at a singular point is shown to be the complement of an affine polar graph. This identification yields the full automorphism group as an affine semisimilarity group and provides explicit extensions to the ambient graph. Maximum independent sets are affine cosets of maximal totally singular subspaces, giving the independence and chromatic numbers. In plus type, Delsarte cliques correspond bijectively to ovoids through the base point, leading to a sharp rank threshold. Over $\mathbb{F}_2$, we determine the exact maximum clique number in every dimension, prove that all maximum cliques form a single orbit, and obtain the core of every first subconstituent. A uniform Witt-extension argument gives a short proof of triple transitivity for the binary local graphs.
