{
  "id": "1708.05396",
  "version": "v1",
  "published": "2017-08-17T18:07:49.000Z",
  "updated": "2017-08-17T18:07:49.000Z",
  "title": "Sufficient conditions for graphs to be $k$-connected, maximally connected and super-connected",
  "authors": [
    "Zhen-Mu Hong",
    "Zheng-Jiang Xia",
    "Fuyuan Chen",
    "Lutz Volkmann"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a connected graph with minimum degree $\\delta(G)$ and vertex-connectivity $\\kappa(G)$. The graph $G$ is $k$-connected if $\\kappa(G)\\geq k$, maximally connected if $\\kappa(G) = \\delta(G)$, and super-connected (or super-$\\kappa$) if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is $k$-connected, maximally connected or super-connected if the number of edges or the spectral radius is large enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-17T18:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40",
      "05C50"
    ],
    "keywords": [
      "sufficient conditions",
      "minimum degree",
      "connected graph",
      "minimum vertex-cut isolates",
      "spectral radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}