{
  "id": "1609.03002",
  "version": "v1",
  "published": "2016-09-10T05:48:35.000Z",
  "updated": "2016-09-10T05:48:35.000Z",
  "title": "Radio number of trees",
  "authors": [
    "Devsi Bantva",
    "Samir Vaidya",
    "Sanming Zhou"
  ],
  "comment": "19 pages, 7 figures. This is the final version accepted in Discrete Applied Mathematics",
  "categories": [
    "math.CO"
  ],
  "abstract": "A radio labeling of a graph $G$ is a mapping $f: V(G) \\rightarrow \\{0, 1, 2, \\ldots\\}$ such that $|f(u)-f(v)|\\geq d + 1 - d(u,v)$ for every pair of distinct vertices $u, v$ of $G$, where $d$ is the diameter of $G$ and $d(u,v)$ the distance between $u$ and $v$ in $G$. The radio number of $G$ is the smallest integer $k$ such that $G$ has a radio labeling $f$ with $\\max\\{f(v) : v \\in V(G)\\} = k$. We give a necessary and sufficient condition for a lower bound on the radio number of trees to be achieved, two other sufficient conditions for the same bound to be achieved by a tree, and an upper bound on the radio number of trees. Using these, we determine the radio number for three families of trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-10T05:48:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C15"
    ],
    "keywords": [
      "radio number",
      "sufficient condition",
      "radio labeling",
      "distinct vertices",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}