{
  "id": "2109.07656",
  "version": "v1",
  "published": "2021-09-16T01:22:02.000Z",
  "updated": "2021-09-16T01:22:02.000Z",
  "title": "The Q-index and connectivity of graphs",
  "authors": [
    "Peng-Li Zhang",
    "Lihua Feng",
    "Weijun Liu",
    "Xiao-Dong Zhang"
  ],
  "comment": "11 pages. arXiv admin note: text overlap with arXiv:2109.07347",
  "categories": [
    "math.CO"
  ],
  "abstract": "A connected graph $G$ is said to be $k$-connected if it has more than $k$ vertices and remains connected whenever fewer than $k$ vertices are deleted. In this paper, for a connected graph $G$ with sufficiently large order, we present a tight sufficient condition for $G$ with fixed minimum degree to be $k$-connected based on the $Q$-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac type condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-16T01:22:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "connectivity",
      "connected graph",
      "corresponding dirac type condition",
      "tight sufficient condition",
      "sufficiently large order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}