{
  "id": "1805.10083",
  "version": "v1",
  "published": "2018-05-25T11:14:31.000Z",
  "updated": "2018-05-25T11:14:31.000Z",
  "title": "Further results on the radio number of trees",
  "authors": [
    "Devsi Bantva"
  ],
  "comment": "7 Pages, CTGTC 2016 conference proceedings paper",
  "journal": "Electronic Notes in Discrete Mathematics, Volume 63, Pages 85-91, 2017",
  "doi": "10.1016/j.endm.2017.11.002",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a finite, connected, undirected graph with diameter $diam(G)$ and $d(u,v)$ denote the distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $f: V(G) \\rightarrow \\{0,1,2,...\\}$ such that $|f(u)-f(v)| \\geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u, v$ of $G$. The radio number of $G$, denoted by $rn(G)$, is the smallest integer $k$ such that $G$ has a radio labeling $f$ with $\\max\\{f(v) : v \\in V(G)\\} = k$. In this paper, we determine the radio number for three families of trees obtained by taking graph operation on a given tree or a family of trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T11:14:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C78"
    ],
    "keywords": [
      "radio number",
      "radio labeling",
      "distinct vertices",
      "smallest integer",
      "graph operation"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}