{
  "id": "1901.08048",
  "version": "v1",
  "published": "2019-01-23T18:58:20.000Z",
  "updated": "2019-01-23T18:58:20.000Z",
  "title": "A general method to obtain the spectrum and local spectra of a graph from its regular partitions",
  "authors": [
    "C. Dalfó",
    "M. A. Fiol"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, we propose a method to obtain all the spectrum, and also the local spectra, of a graph $\\Gamma$ from the quotient matrices of some of its regular partitions. As examples, it is shown how to find the eigenvalues and (local) multiplicities of walk-regular, distance-regular, and distance-biregular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-23T18:58:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05C50"
    ],
    "keywords": [
      "regular partition",
      "local spectra",
      "general method",
      "adjacency matrix",
      "quotient matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}