{
  "id": "2407.10288",
  "version": "v1",
  "published": "2024-07-14T18:12:36.000Z",
  "updated": "2024-07-14T18:12:36.000Z",
  "title": "On vertex peripherians and Wiener index of graphs with fixed number of cut vertices",
  "authors": [
    "Dinesh Pandey"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The distance of a vertex in a graph is the sum of distances from that vertex to all other vertices of the graph. The Wiener index of a graph is the sum of distances between all its unordered pairs of vertices. A graph has been obtained that contains a vertex achieving the maximum distance among all graphs on $n$ vertices with fixed number of cut vertices. Further the graphs having maximum Wiener index among all graphs on $n$ vertices with at most $3$ cut vertices have been characterised.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-14T18:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C09",
      "05C12",
      "05C35"
    ],
    "keywords": [
      "cut vertices",
      "fixed number",
      "vertex peripherians",
      "maximum wiener index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}