{
  "id": "1512.01377",
  "version": "v1",
  "published": "2015-12-04T11:44:03.000Z",
  "updated": "2015-12-04T11:44:03.000Z",
  "title": "On connected simple graphs and their degree sequences",
  "authors": [
    "Jonathan McLaughlin"
  ],
  "comment": "9 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence can only be realised as a connected graph. A matrix is introduced whose non-empty entries partition the set of connected graphs. The note concludes with a result relating the number of edges in a simple graph to the connectedness of the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-04T11:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40"
    ],
    "keywords": [
      "connected simple graph",
      "degree sequence",
      "connected graph",
      "non-empty entries partition",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151201377M"
    }
  }
}