{
  "id": "1905.06595",
  "version": "v1",
  "published": "2019-05-16T08:29:29.000Z",
  "updated": "2019-05-16T08:29:29.000Z",
  "title": "Trees whose even-degree vertices induce a path are antimagic",
  "authors": [
    "Antoni Lozano",
    "Mercè Mora",
    "Carlos Seara",
    "Joaquín Tey"
  ],
  "comment": "7 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "An antimagic labeling a connected graph $G$ is a bijection from the set of edges $E(G)$ to $\\{1,2,\\dots,|E(G)|\\}$ such that all vertex sums are pairwise distinct, where the vertex sum at vertex $v$ is the sum of the labels assigned to edges incident to $v$. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than $K_2$ is antimagic; however, the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Discrete Math. 331 (2014) 9--14].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-16T08:29:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C05"
    ],
    "keywords": [
      "even-degree vertices induce",
      "vertex sum",
      "conjecture remains open",
      "antimagic labeling",
      "simple connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}