{
  "id": "1511.05843",
  "version": "v1",
  "published": "2015-11-18T15:46:23.000Z",
  "updated": "2015-11-18T15:46:23.000Z",
  "title": "The Hopf Algebra of graph invariants",
  "authors": [
    "Nicolas Borie"
  ],
  "comment": "12 pages, submitted to FPSAC2016",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that these series can be evaluated on graphs and count occurrences of subgraphs. We establish a criterion for the isomorphism test of two simple graphs by means of occurrence counting of subgraphs. This criterion is deduced from algebraic relations between elements of our algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-18T15:46:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hopf algebra",
      "graph invariants",
      "simple graph isomorphism problem",
      "formal power series",
      "algebraic relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105843B"
    }
  }
}