{
  "id": "1701.08537",
  "version": "v1",
  "published": "2017-01-30T10:49:11.000Z",
  "updated": "2017-01-30T10:49:11.000Z",
  "title": "Locating-Dominating Sets and Identifying Codes of a Graph Associated to a Finite Vector Space",
  "authors": [
    "Muhammad Murtaza",
    "Imran Javaid",
    "Muhammad Fazil"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das \\cite{Das}, such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-dominating sets and identifying codes, which are closely related concepts for this purpose. These sets consist of a dominating set of graph such that every vertex is uniquely identified by its neighborhood within the dominating sets. We find the location-domination number and the identifying number of the graph and study the exchange property for locating-dominating sets and identifying codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-30T10:49:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C25",
      "05C69"
    ],
    "keywords": [
      "finite vector space",
      "locating-dominating sets",
      "identifying codes",
      "sets consist",
      "location-domination number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}