{
  "id": "1805.10084",
  "version": "v1",
  "published": "2018-05-25T11:27:16.000Z",
  "updated": "2018-05-25T11:27:16.000Z",
  "title": "Radio number for middle graph of paths",
  "authors": [
    "Devsi Bantva"
  ],
  "comment": "8 Pages, CTGTC 2016 conference proceedings paper",
  "journal": "Electronic Notes in Discrete Mathematics, Volume 63, Pages 93-100, 2017",
  "doi": "10.1016/j.endm.2017.11.003",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a connected graph $G$, let $diam(G)$ and $d(u,v)$ denote the diameter of $G$ and distance between $u$ and $v$ in $G$. A radio labeling of a graph $G$ is a mapping $\\varphi : V(G) \\rightarrow \\{0,1,2,...\\}$ such that $|\\varphi(u)-\\varphi(v)| \\geq diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u, v$ of $G$. The span of $\\varphi$ is defined as span($\\varphi$) = $\\max\\{|\\varphi(u)-\\varphi(v)| : u, v \\in V(G)\\}$. The radio number $rn(G)$ of $G$ is defined as $rn(G)$ = $\\min\\{$span($\\varphi$) : $\\varphi$ is a radio labeling of $G\\}$. In this paper, we determine the radio number for middle graph of paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-25T11:27:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C78"
    ],
    "keywords": [
      "radio number",
      "middle graph",
      "radio labeling",
      "distinct vertices"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}