English

Separating rank 3 graphs

Combinatorics 2023-05-24 v2

Abstract

We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not QI\mathbb{Q}\mathrm{I}, groups of affine type.

Keywords

Cite

@article{arxiv.2211.02326,
  title  = {Separating rank 3 graphs},
  author = {John Bamberg and Michael Giudici and Jesse Lansdown and Gordon F. Royle},
  journal= {arXiv preprint arXiv:2211.02326},
  year   = {2023}
}

Comments

Added acknowledgements and noted the third author's change of institution

R2 v1 2026-06-28T05:10:29.686Z