{
  "id": "1803.01312",
  "version": "v1",
  "published": "2018-03-04T07:33:50.000Z",
  "updated": "2018-03-04T07:33:50.000Z",
  "title": "Component edge connectivity of the folded hypercube",
  "authors": [
    "Shuli Zhao",
    "Weihua Yang"
  ],
  "comment": "The work was included in the MS thesis of the first author in [On the component connectiviy of hypercubes and folded hypercubes, MS Thesis at Taiyuan University of Technology, 2017]",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $g$-component edge connectivity $c\\lambda_g(G)$ of a non-complete graph $G$ is the minimum number of edges whose deletion results in a graph with at least $g$ components. In this paper, we determine the component edge connectivity of the folded hypercube $c\\lambda_{g+1}(FQ_{n})=(n+1)g-(\\sum\\limits_{i=0}^{s}t_i2^{t_i-1}+\\sum\\limits_{i=0}^{s} i\\cdot 2^{t_i})$ for $g\\leq 2^{[\\frac{n+1}2]}$ and $n\\geq 5$, where $g$ be a positive integer and $g=\\sum\\limits_{i=0}^{s}2^{t_i}$ be the decomposition of $g$ such that $t_0=[\\log_{2}{g}],$ and $t_i=[\\log_2({g-\\sum\\limits_{r=0}^{i-1}2^{t_r}})]$ for $i\\geq 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-04T07:33:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "component edge connectivity",
      "folded hypercube",
      "non-complete graph",
      "minimum number",
      "deletion results"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}