{
  "id": "2107.03161",
  "version": "v1",
  "published": "2021-07-07T11:40:13.000Z",
  "updated": "2021-07-07T11:40:13.000Z",
  "title": "On Magic Distinct Labellings of Simple Graphs",
  "authors": [
    "Guoce Xin",
    "Xinyu Xu",
    "Chen Zhang",
    "Yueming Zhong"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v\\in V$, the sum of labels of all edges incident to $v$ is equal to the same number $s$. Stanley gave remarkable results on magic labellings, but the distinct labelling case is much more complicated. We consider the complete construction of all magic labellings of a given graph $G$. The idea is illustrated in detail by dealing with three regular graphs. We give combinatorial proofs. The structure result was used to enumerate the corresponding magic distinct labellings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T11:40:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "11D04",
      "05C78"
    ],
    "keywords": [
      "simple graphs",
      "magic labelling",
      "corresponding magic distinct labellings",
      "stanley gave",
      "structure result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}