{
  "id": "1606.03726",
  "version": "v1",
  "published": "2016-06-12T15:08:26.000Z",
  "updated": "2016-06-12T15:08:26.000Z",
  "title": "Arithmetical structures of graphs II: Graphs with connectivity one",
  "authors": [
    "Hugo Corrales",
    "Carlos E. Valencia"
  ],
  "comment": "10 pages. Comments are welcome!",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We give a description of the arithmetical structures of a graph G with a cut vertex v in function of the arithmetical structures of its blocks. More precisely, if G_1,...,G_s are the induced subgraphs of G obtained from each of the connected components of G-v by adding the vertex v and its incident edges, then the arithmetical structures of G are in correspondence with the v-rational arithmetical structures of the G_i's. We introduce a key concept, of rational arithmetical structure, which correspond to an arithmetical structure were some integer conditions are relaxed. This concept is useful in a wide number of situations, as in the case of graphs with twin vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-12T15:08:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B36",
      "14C17"
    ],
    "keywords": [
      "connectivity",
      "wide number",
      "twin vertices",
      "integer conditions",
      "v-rational arithmetical structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}