{
  "id": "2101.06877",
  "version": "v1",
  "published": "2021-01-18T05:06:08.000Z",
  "updated": "2021-01-18T05:06:08.000Z",
  "title": "Spectra of strongly Deza graphs",
  "authors": [
    "Saieed Akbari",
    "Willem H. Haemers",
    "Mohammad Ali Hosseinzadeh",
    "Vladislav V. Kabanov",
    "Elena V. Konstantinova",
    "Leonid Shalaginov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A Deza graph $G$ with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_A$ and $G_B$ of a Deza graph $G$ are defined on the vertex set of $G$ such that every two distinct vertices are adjacent in $G_A$ or $G_B$ if and only if they have $a$ or $b$ common neighbours, respectively. A strongly Deza graph is a Deza graph with strongly regular children. In this paper we give a spectral characterisation of strongly Deza graphs, show relationships between eigenvalues, and study strongly Deza graphs which are distance-regular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-18T05:06:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distinct vertices",
      "common neighbours",
      "study strongly deza graphs",
      "vertex set",
      "regular graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}