{
  "id": "1703.03581",
  "version": "v1",
  "published": "2017-03-10T08:54:47.000Z",
  "updated": "2017-03-10T08:54:47.000Z",
  "title": "Some spectral properties of chain graphs",
  "authors": [
    "Ebrahim Ghorbani"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is called a chain graph if it is bipartite and the neighborhoods of the vertices in each color class form a chain with respect to inclusion. Alazemi, Andeli\\'c and Simi\\'c conjectured that no chain graph shares a non-zero (adjacency) eigenvalue with its vertex-deleted subgraphs. We disprove this conjecture. However, we show that the assertion holds for subgraphs obtained by deleting vertices of maximum degrees in either of color classes. We also give a simple proof for the fact that chain graphs have no eigenvalue in the interval $(0,1/2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-10T08:54:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "spectral properties",
      "color class form",
      "chain graph shares",
      "simple proof",
      "assertion holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}