{
  "id": "0911.0126",
  "version": "v1",
  "published": "2009-11-01T04:33:06.000Z",
  "updated": "2009-11-01T04:33:06.000Z",
  "title": "On the Spectrum of Middle-Cubes",
  "authors": [
    "Ke Qiu",
    "Rong Qiu",
    "Yong Jiang",
    "Jian Shen"
  ],
  "comment": "8 Pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A middle-cube is an induced subgraph consisting of nodes at the middle two layers of a hypercube. The middle-cubes are related to the well-known Revolving Door (Middle Levels) conjecture. We study the middle-cube graph by completely characterizing its spectrum. Specifically, we first present a simple proof of its spectrum utilizing the fact that the graph is related to Johnson graphs which are distance-regular graphs and whose eigenvalues can be computed using the association schemes. We then give a second proof from a pure graph theory point of view without using its distance regular property and the technique of association schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-01T04:33:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "association schemes",
      "pure graph theory point",
      "distance regular property",
      "second proof",
      "middle levels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0126Q"
    }
  }
}