{
  "id": "2409.10255",
  "version": "v1",
  "published": "2024-09-16T13:06:37.000Z",
  "updated": "2024-09-16T13:06:37.000Z",
  "title": "The maximum size of a nonhamiltonian-connected graph with given order and minimum degree",
  "authors": [
    "Leilei Zhang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we determine the maximum size of a nonhamiltonian-connected graph with prescribed order and minimum degree. We also characterize the extremal graphs that attain this maximum size. This work generalizes a previous result obtained by Ore [ J. Math. Pures Appl. 42 (1963) 21-27] and further extends a theorem proved by Ho, Lin, Tan, Hsu, and Hsu [Appl. Math. Lett. 23 (2010) 26-29]. As a corollary of our main result, we determine the maximum size of a $k$-connected nonhamiltonian-connected graph with a given order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-16T13:06:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum size",
      "nonhamiltonian-connected graph",
      "minimum degree",
      "main result",
      "work generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}