{
  "id": "1008.0595",
  "version": "v2",
  "published": "2010-08-03T17:19:49.000Z",
  "updated": "2012-05-22T02:47:18.000Z",
  "title": "Induced Subgraphs of Johnson Graphs",
  "authors": [
    "Ramin Naimi",
    "Jeffrey Shaw"
  ],
  "comment": "12 pages, 4 figures",
  "journal": "Involve, a Journal of Mathematics 5-1 (2012), 25-37",
  "doi": "10.2140/involve.2012.5.25",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Johnson graph J(n,N) is defined as the graph whose vertices are the n-subsets of the set {1,2,...,N}, where two vertices are adjacent if they share exactly n - 1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. We give some necessary conditions and some sufficient conditions for a graph to be JIS, including: in a JIS graph, any two maximal cliques share at most two vertices; all trees, cycles, and complete graphs are JIS; disjoint unions and Cartesian products of JIS graphs are JIS; every JIS graph of order n is an induced subgraph of J(m,2n) for some m <= n. This last result gives an algorithm for deciding if a graph is JIS. We also show that all JIS graphs are edge move distance graphs, but not vice versa.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-22T02:47:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced subgraph",
      "jis graph",
      "edge move distance graphs",
      "maximal cliques share",
      "vice versa"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0595N"
    }
  }
}