{
  "id": "2104.08498",
  "version": "v1",
  "published": "2021-04-17T09:42:23.000Z",
  "updated": "2021-04-17T09:42:23.000Z",
  "title": "Extremal digraphs avoiding distinct walks of length 3 with the same endpoints",
  "authors": [
    "Zejun Huang",
    "Zhenhua Lyu"
  ],
  "comment": "11 pages,2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we determine the maximum size of digraphs on $n$ vertices in which there are no two distinct walks of length $3$ with the same initial vertex and the same terminal vertex. The digraphs attaining this maximum size are also characterized. Combining this with previous results, we obtain a full solution to a problem proposed by X. Zhan in 2007.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-17T09:42:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C35"
    ],
    "keywords": [
      "extremal digraphs avoiding distinct walks",
      "maximum size",
      "initial vertex",
      "terminal vertex",
      "full solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}