{
  "id": "1903.05613",
  "version": "v1",
  "published": "2019-03-13T17:27:03.000Z",
  "updated": "2019-03-13T17:27:03.000Z",
  "title": "A lower bound for the radio number of graphs",
  "authors": [
    "Devsi Bantva"
  ],
  "comment": "13 pages, CALDAM 2019 conference proceeding paper",
  "journal": "In: Pal S., Vijayakumar A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science, vol 11394, pp 161-173. Springer, Cham",
  "doi": "10.1007/978-3-030-11509-8_14",
  "categories": [
    "math.CO"
  ],
  "abstract": "A radio labeling of a graph $G$ is a mapping $\\vp : V(G) \\rightarrow \\{0, 1, 2,...\\}$ such that $|\\vp(u)-\\vp(v)|\\geq \\diam(G) + 1 - d(u,v)$ for every pair of distinct vertices $u,v$ of $G$, where $\\diam(G)$ and $d(u,v)$ are the diameter of $G$ and distance between $u$ and $v$ in $G$, respectively. The radio number $\\rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with $\\max\\{\\vp(v):v \\in V(G)\\}$ = $k$. In this paper, we slightly improve the lower bound for the radio number of graphs given by Das \\emph{et al.} in [5] and, give necessary and sufficient condition to achieve the lower bound. Using this result, we determine the radio number for cartesian product of paths $P_{n}$ and the Peterson graph $P$. We give a short proof for the radio number of cartesian product of paths $P_{n}$ and complete graphs $K_{m}$ given by Kim \\emph{et al.} in [6].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-13T17:27:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C15",
      "05C12"
    ],
    "keywords": [
      "radio number",
      "lower bound",
      "cartesian product",
      "distinct vertices",
      "radio labeling"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}