{
  "id": "2306.08369",
  "version": "v1",
  "published": "2023-06-14T09:01:07.000Z",
  "updated": "2023-06-14T09:01:07.000Z",
  "title": "Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique",
  "authors": [
    "Alexander L. Gavrilyuk",
    "Vladislav V. Kabanov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph $\\mathsf{Sp}(2d,q)$. In this paper, we determine the parameters of strongly regular graphs which admit a decomposition into a divisible design graph and a coclique attaining the Hoffman bound. In particular, it is shown that when the least eigenvalue of such a strongly regular graph is a prime power, its parameters coincide with those of the complement of $\\mathsf{Sp}(2d,q)$. Furthermore, a generalization of the construction is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-14T09:01:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divisible design graph",
      "strongly regular graphs decomposable",
      "hoffman coclique",
      "construction produces strongly regular graphs",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}