{
  "id": "1508.07608",
  "version": "v1",
  "published": "2015-08-30T18:11:49.000Z",
  "updated": "2015-08-30T18:11:49.000Z",
  "title": "Relative complements and a `switch'-classification of simple graphs",
  "authors": [
    "Elżbieta Błaszko",
    "Małgorzata Prażmowska",
    "Krzysztof Prażmowski"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In the paper we introduce and study a classification of finite (simple, undirected, loopless) graphs with respect to a switch-equivalence (`local-complement' equivalence of \\cite{pascvebl}, an analogue of the complement-equivalence of \\cite{conell}). In the paper we propose a simple inductive method to compute the number of switch-types of graphs on $n$ vertices and we show that there are exactly 16 such types of graphs on 6 vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-30T18:11:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C76"
    ],
    "keywords": [
      "simple graphs",
      "relative complements",
      "simple inductive method",
      "local-complement",
      "complement-equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807608B"
    }
  }
}