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PreprintCC BY 4.0arXiv

On the weight distribution bound for the negative eigenvalue of polar collinearity graphs

  • Sam Adriaensen
  • Jim Wittebol
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Abstract

The weight distribution bound gives a lower bound on the weight of eigenvectors for eigenvalues of distance-regular graphs. In this note, we study when the weight distribution bound is tight for the negative eigenvalue of collinearity graphs of finite embedded polar spaces, and elliptic and hyperbolic affine polar graphs. We give a complete classification of eigenvectors meeting the weight distribution bound.

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Cite

BibTeXRIS
BibTeX
@misc{adriaensen2026weight,
  title = {{On the weight distribution bound for the negative eigenvalue of polar collinearity graphs}},
  author = {Sam Adriaensen and Jim Wittebol},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.28153},
  eprint = {2607.28153},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28153},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the weight distribution bound for the negative eigenvalue of polar collinearity graphs
AU  - Sam Adriaensen
AU  - Jim Wittebol
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2607.28153
UR  - https://arxiv.org/abs/2607.28153
AB  - The weight distribution bound gives a lower bound on the weight of eigenvectors for eigenvalues of distance-regular graphs. In this note, we study when the weight distribution bound is tight for the negative eigenvalue of collinearity graphs of finite embedded polar spaces, and elliptic and hyperbolic affine polar graphs. We give a complete classification of eigenvectors meeting the weight distribution bound.
ER  -