{
  "id": "1102.5181",
  "version": "v1",
  "published": "2011-02-25T07:58:03.000Z",
  "updated": "2011-02-25T07:58:03.000Z",
  "title": "On the edge connectivity of direct products with dense graphs",
  "authors": [
    "Wei Wang",
    "Zhidan Yan"
  ],
  "comment": "8 pages, submited to discrete math",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\kappa'(G)$ be the edge connectivity of $G$ and $G\\times H$ the direct product of $G$ and $H$. Let $H$ be an arbitrary dense graph with minimal degree $\\delta(H)>|H|/2$. We prove that for any graph $G$, $\\kappa'(G\\times H)=\\textup{min}\\{2\\kappa'(G)e(H),\\delta(G)\\delta(H)\\}$, where $e(H)$ denotes the number of edges in $H$. In addition, the structure of minimum edge cuts is described. As an application, we present a necessary and sufficient condition for $G\\times K_n(n\\ge3)$ to be super edge connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-25T07:58:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge connectivity",
      "direct product",
      "arbitrary dense graph",
      "minimum edge cuts",
      "minimal degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5181W"
    }
  }
}