{
  "id": "1602.04089",
  "version": "v1",
  "published": "2016-02-12T15:55:08.000Z",
  "updated": "2016-02-12T15:55:08.000Z",
  "title": "On minimum identifying codes in some Cartesian product graphs",
  "authors": [
    "Douglas F. Rall",
    "Kirsti Wash"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in a graph $G$ is called the ID code number of $G$ and is denoted $\\gid(G)$. In this paper, we give upper and lower bounds for the ID code number of the prism of a graph, or $G\\Box K_2$. In particular, we show that $\\gid(G \\Box K_2) \\ge \\gid(G)$ and we show that this bound is sharp. We also give upper and lower bounds for the ID code number of grid graphs and a general upper bound for $\\gid(G\\Box K_2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-12T15:55:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian product graphs",
      "minimum identifying codes",
      "id code number",
      "lower bounds",
      "general upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204089R"
    }
  }
}