{
  "id": "2411.18930",
  "version": "v1",
  "published": "2024-11-28T05:36:53.000Z",
  "updated": "2024-11-28T05:36:53.000Z",
  "title": "The Minimal (Edge) Connectivity of Some Graphs of Finite Groups",
  "authors": [
    "Siddharth Malviy",
    "Vipul Kakkar"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we classify all the finite groups $G$ such that the commuting graph $\\Gamma_C(G)$, order-sum graph $\\Gamma_{OS}(G)$ and non-inverse graph $\\Gamma_{NI}(G)$ are minimally edge connected graphs. We also classify all the finite groups $G$ for that, these graphs are minimally connected. We also classify some groups for that the co-prime graph $\\Gamma_{CP}(G)$ has minimal edge connectedness. In final part, we classify all the finite groups $G$ for that co-prime graph $\\Gamma_{CP}(G)$ is minimally connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-28T05:36:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite groups",
      "connectivity",
      "co-prime graph",
      "minimal edge connectedness",
      "non-inverse graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}