{
  "id": "1505.05811",
  "version": "v1",
  "published": "2015-05-21T18:01:43.000Z",
  "updated": "2015-05-21T18:01:43.000Z",
  "title": "The Metric Dimension of The Tensor Product of Cliques",
  "authors": [
    "H. Amraei",
    "H. R. Maimani",
    "A. Seify",
    "A. Zaeembashi"
  ],
  "comment": "9 pages, no figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph and $W=\\{ w_1, w_2, \\ldots, w_k \\} \\subseteq V(G)$ be an ordered set. For every vertex $v$, the metric representation of $v$ with respect to $W$ is an ordered $k$-vector defined as $r(v|W):=(d(v,w_1), d(v,w_2), \\ldots, d(v,w_k))$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The set $W$ is called a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. The minimum cardinality of a resolving set for $G$ is its metric dimension and is denoted by $dim(G)$. In this paper, we study the metric dimension of tensor product of cliques and prove some bounds. Then we determine the metric dimension of tensor product of two cliques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T18:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C69"
    ],
    "keywords": [
      "metric dimension",
      "tensor product",
      "resolving set",
      "minimum cardinality",
      "metric representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505811A"
    }
  }
}