{
  "id": "0909.3252",
  "version": "v1",
  "published": "2009-09-17T15:26:51.000Z",
  "updated": "2009-09-17T15:26:51.000Z",
  "title": "Automorphism groups of a graph and a vertex-deleted subgraph",
  "authors": [
    "Stephen G. Hartke",
    "Hannah Kolb",
    "Jared Nishikawa",
    "Derrick Stolee"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question of which pairs of groups can be represented as the automorphism groups of a graph and a vertex-deleted subgraph. This, and more surprisingly the analogous question for edge-deleted subgraphs, are answered in the most positive sense using concrete constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-17T15:26:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C60"
    ],
    "keywords": [
      "automorphism groups",
      "vertex-deleted subgraph",
      "concrete constructions",
      "reconstruction conjecture",
      "isomorph-free generation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3252H"
    }
  }
}