{
  "id": "1506.03442",
  "version": "v1",
  "published": "2015-06-10T19:57:28.000Z",
  "updated": "2015-06-10T19:57:28.000Z",
  "title": "On global location-domination in bipartite graphs",
  "authors": [
    "Carmen Hernando",
    "Merce Mora",
    "Ignacio M. Pelayo"
  ],
  "comment": "13 pages, 7 figures. arXiv admin note: text overlap with arXiv:1312.0772",
  "categories": [
    "math.CO"
  ],
  "abstract": "A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the \\emph{location-domination number} $\\lambda(G)$. An LD-set $S$ of a graph $G$ is \\emph{global} if it is an LD-set of both $G$ and its complement $\\overline{G}$. The \\emph{global location-domination number} $\\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. For any LD-set $S$ of a given graph $G$, the so-called \\emph{S-associated graph} $G^S$ is introduced. This edge-labeled bipartite graph turns out to be very helpful to approach the study of LD-sets in graphs, particularly when $G$ is bipartite. This paper is mainly devoted to the study of relationships between global LD-sets, LD-codes and the location-domination number in a graph $G$ and its complement $\\overline{G}$, when $G$ is bipartite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-10T19:57:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69"
    ],
    "keywords": [
      "global location-domination",
      "minimum cardinality",
      "location-domination number",
      "global ld-set",
      "edge-labeled bipartite graph turns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150603442H"
    }
  }
}