{
  "id": "1404.5192",
  "version": "v1",
  "published": "2014-04-21T13:47:34.000Z",
  "updated": "2014-04-21T13:47:34.000Z",
  "title": "On the power graph of a finite group",
  "authors": [
    "Min Feng",
    "Xuanlong Ma",
    "Kaishun Wang"
  ],
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The power graph $\\mathcal P_G$ of a finite group $G$ is the graph with the vertex set $G$, where two elements are adjacent if one is a power of the other. We first show that $\\mathcal P_G$ has an transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups (under usual inclusion) to characterise the structure of $\\mathcal P_G$. Finally, the closed formula for the metric dimension of $\\mathcal P_G$ is established. As an application, we compute the metric dimension of the power graph of a cyclic group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-21T13:47:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power graph",
      "finite group",
      "metric dimension",
      "vertex set",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5192F"
    }
  }
}