{
  "id": "1901.00355",
  "version": "v1",
  "published": "2019-01-02T13:30:45.000Z",
  "updated": "2019-01-02T13:30:45.000Z",
  "title": "On Radio Number of Stacked-Book Graphs",
  "authors": [
    "Tayo Charles Adefokun",
    "Deborah Olayide Ajayi"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Stacked-book graph $G_{m,n}$ results from the Cartesian product of a star graph $S_m$ and path $P_n$, where $m$ and $n$ are the orders of $S_m$ and $P_n$ respectively. A radio labeling problem of a simple and connected graph, $G$, involves a non-negative integer function $f:V(G)\\rightarrow \\mathbb Z^+$ on the vertex set $V(G)$ of G, such that for all $u,v \\in V(G)$, $|f(u)-f(v)| \\geq \\textmd{diam}(G)+1-d(u,v)$, where $\\textmd {diam}(G)$ is the diameter of $G$ and $d(u,v)$ is the shortest distance between $u$ and $v$. Suppose that $f_{min}$ and $f_{max}$ are the respective least and largest values of $f$ on $V(G)$, then, span$f$, the absolute difference of $f_{min}$ and $f_{max}$, is the span of $f$ while the radio number $rn(G)$ of $G$ is the least value of span$f$ over all the possible radio labels on $V(G)$. In this paper, we obtain the radio number for the stacked-book graph $G_{m,n}$ where $m \\geq 4$ and $n$ is even, and obtain bounds for $m=3$ which improves existing upper and lower bounds for $G_{m,n}$ where $m=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-02T13:30:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78",
      "05C15"
    ],
    "keywords": [
      "stacked-book graph",
      "radio number",
      "radio labels",
      "cartesian product",
      "absolute difference"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}