{
  "id": "1111.1200",
  "version": "v1",
  "published": "2011-11-04T18:08:42.000Z",
  "updated": "2011-11-04T18:08:42.000Z",
  "title": "Spectra of Coronae",
  "authors": [
    "Cam McLeman",
    "Erin McNicholas"
  ],
  "comment": "9 pages",
  "journal": "Linear Algebra and its Applications, Volume 435, no. 5, (2011)",
  "doi": "10.1016/j.laa.2011.02.007",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a new invariant, the coronal of a graph, and use it to compute the spectrum of the corona $G\\circ H$ of two graphs $G$ and $H$. In particular, we show that this spectrum is completely determined by the spectra of $G$ and $H$ and the coronal of $H$. Previous work has computed the spectrum of a corona only in the case that $H$ is regular. We then explicitly compute the coronals for several families of graphs, including regular graphs, complete $n$-partite graphs, and paths. Finally, we use the corona construction to generate many infinite families of pairs of cospectral graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-04T18:08:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C76"
    ],
    "keywords": [
      "cospectral graphs",
      "regular graphs",
      "partite graphs",
      "corona construction",
      "infinite families"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1200M"
    }
  }
}