First Subconstituents of Orthogonal Graphs in Even Characteristic:Automorphisms, Cliques, Cores, and Binary Triple Transitivity
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Zhou, Kai, Wu, Hongfeng
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214110788