First Subconstituents of Orthogonal Graphs in Even Characteristic:Automorphisms, Cliques, Cores, and Binary Triple Transitivity
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 𝔽2, 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.
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BibTeX
@misc{zhou2026first,
title = {{First Subconstituents of Orthogonal Graphs in Even Characteristic:Automorphisms, Cliques, Cores, and Binary Triple Transitivity}},
author = {Kai Zhou and Hongfeng Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26240},
eprint = {2609.26240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26240},
}
RIS
TY - UNPB
TI - First Subconstituents of Orthogonal Graphs in Even Characteristic:Automorphisms, Cliques, Cores, and Binary Triple Transitivity
AU - Kai Zhou
AU - Hongfeng Wu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26240
UR - https://arxiv.org/abs/2609.26240
AB - 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 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.
ER -