{
  "id": "2212.07319",
  "version": "v1",
  "published": "2022-12-14T16:29:23.000Z",
  "updated": "2022-12-14T16:29:23.000Z",
  "title": "Spectral properties of a class of cographs",
  "authors": [
    "Santanu Mandal",
    "Ranjit Mehatari"
  ],
  "comment": "15 pages, 1figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "We explore several properties of the adjacency matrix of a class of connected cographs. Those cographs can be defined by a finite sequence of natural numbers. Using that sequence we obtain multiplicity of the eigenvalues $0,-1$, inertia for the adjacency matrix of the cograph under consideration. We find an eigenvalue-free interval for such graphs which is better than previously obtained interval $(-1,0)$. Finally, we establish a suitable formula for the characteristic polynomial of the adjacency matrix for such graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T16:29:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral properties",
      "adjacency matrix",
      "natural numbers",
      "finite sequence",
      "characteristic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}