{
  "id": "1812.09087",
  "version": "v1",
  "published": "2018-12-21T12:44:32.000Z",
  "updated": "2018-12-21T12:44:32.000Z",
  "title": "Hopf algebra structure on graph",
  "authors": [
    "Shoujun Xu",
    "Xiaomeng Wang",
    "Xing Gao"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "In this paper, we construct a bialgebraic and further a Hopf algebraic structure on top of subgraphs of a given graph. Further, we give the dual structure of this Hopf algebraic structure. We study the algebra morphisms induced by graph homomorphisms, and obtain a functor from a graph category to an algebra category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-21T12:44:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16W99",
      "16T05",
      "16T10",
      "16T30"
    ],
    "keywords": [
      "hopf algebra structure",
      "hopf algebraic structure",
      "algebra morphisms",
      "algebra category",
      "graph category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}