{
  "id": "2211.02326",
  "version": "v1",
  "published": "2022-11-04T09:01:52.000Z",
  "updated": "2022-11-04T09:01:52.000Z",
  "title": "Separating rank 3 graphs",
  "authors": [
    "John Bamberg",
    "Michael Giudici",
    "Jesse Lansdown",
    "Gordon F. Royle"
  ],
  "categories": [
    "math.CO"
  ],
  "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 $\\mathbb{Q}\\mathrm{I}$, groups of affine type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-04T09:01:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05C69",
      "20B15",
      "05C50",
      "05E18"
    ],
    "keywords": [
      "separating rank",
      "hoffman bound",
      "affine type",
      "notoriously hard cases",
      "consequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}