{
  "id": "1312.4973",
  "version": "v1",
  "published": "2013-12-17T21:05:42.000Z",
  "updated": "2013-12-17T21:05:42.000Z",
  "title": "The metric dimension of small distance-regular and strongly regular graphs",
  "authors": [
    "Robert F. Bailey"
  ],
  "comment": "17 pages, 15 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "A {\\em resolving set} for a graph $\\Gamma$ is a collection of vertices $S$, chosen so that for each vertex $v$, the list of distances from $v$ to the members of $S$ uniquely specifies $v$. The {\\em metric dimension} of $\\Gamma$ is the smallest size of a resolving set for $\\Gamma$. A graph is {\\em distance-regular} if, for any two vertices $u,v$ at each distance $i$, the number of neighbours of $v$ at each possible distance from $u$ (i.e. $i-1$, $i$ or $i+1$) depends only on the distance $i$, and not on the choice of vertices $u,v$. The class of distance-regular graphs includes all distance-transitive graphs and all strongly regular graphs. In this paper, we present the results of computer calculations which have found the metric dimension of all distance-regular graphs on up to 34 vertices, low-valency distance transitive graphs on up to 100 vertices, strongly regular graphs on up to 45 vertices, rank-$3$ strongly regular graphs on under 100 vertices, as well as certain other distance-regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T21:05:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05C12",
      "05C25",
      "20B40",
      "05-04"
    ],
    "keywords": [
      "strongly regular graphs",
      "metric dimension",
      "small distance-regular",
      "distance-regular graphs",
      "low-valency distance transitive graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4973B"
    }
  }
}