{
  "id": "1709.05152",
  "version": "v1",
  "published": "2017-09-15T11:06:21.000Z",
  "updated": "2017-09-15T11:06:21.000Z",
  "title": "Locating-Dominating Sets of Functigraphs",
  "authors": [
    "Muhammad Murtaza",
    "Muhammad Fazil",
    "Imran Javaid",
    "Hira Benish"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A locating-dominating set of a graph $G$ is a dominating set of $G$ such that every vertex of $G$ outside the dominating set is uniquely identified by its neighborhood within the dominating set. The location-domination number of $G$ is the minimum cardinality of a locating-dominating set in $G$. Let $G_{1}$ and $G_{2}$ be the disjoint copies of a graph $G$ and $f:V(G_{1})\\rightarrow V(G_{2})$ be a function. A functigraph $F^f_{G}$ consists of the vertex set $V(G_{1})\\cup V(G_{2})$ and the edge set $E(G_{1})\\cup E(G_{2})\\cup \\{uv:v=f(u)\\}$. In this paper, we study the variation of the location-domination number in passing from $G$ to $F^f_{G}$ and find its sharp lower and upper bounds. We also study the location-domination number of functigraphs of the complete graphs for all possible definitions of the function $f$. We also obtain the location-domination number of functigraphs of a family of spanning subgraph of the complete graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T11:06:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C12"
    ],
    "keywords": [
      "locating-dominating set",
      "location-domination number",
      "functigraph",
      "complete graphs",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}