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

Sam Adriaensen; Jim Wittebol

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

Combinatorics 2026-07-30 v1

Authors: Sam Adriaensen , Jim Wittebol

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.

Keywords

weight distribution bound polar collinearity graph distance-regular graph negative eigenvalue finite embedded polar space

Cite

@article{arxiv.2607.28153,
  title  = {On the weight distribution bound for the negative eigenvalue of polar collinearity graphs},
  author = {Sam Adriaensen and Jim Wittebol},
  journal= {arXiv preprint arXiv:2607.28153},
  year   = {2026}
}

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7 pages