{
  "id": "1905.11254",
  "version": "v1",
  "published": "2019-05-24T15:28:45.000Z",
  "updated": "2019-05-24T15:28:45.000Z",
  "title": "On the $g$-good-neighbor connectivity of graphs",
  "authors": [
    "Zhao Wang",
    "Yaping Mao",
    "Sun-Yuan Hsieh",
    "Jichang Wu"
  ],
  "comment": "14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1904.06527; text overlap with arXiv:1609.08885, arXiv:1612.05381 by other authors",
  "categories": [
    "math.CO"
  ],
  "abstract": "Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\\`{a}brega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\\leq \\kappa^g(G)\\leq n-2g-2$ for $0\\leq g\\leq \\left\\{\\Delta(G),\\left\\lfloor \\frac{n-3}{2}\\right\\rfloor\\right\\}$, and graphs with $\\kappa^g(G)=1,2$ and trees with $\\kappa^g(T_n)=n-t$ for $4\\leq t\\leq \\frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T15:28:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "good-neighbor connectivity",
      "important parameters",
      "fault tolerant",
      "interconnection network",
      "extremal results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}