{
  "id": "2104.02266",
  "version": "v1",
  "published": "2021-04-06T03:19:30.000Z",
  "updated": "2021-04-06T03:19:30.000Z",
  "title": "A Sharp Upper Bound for the Boundary Independence Broadcast Number of a Tree",
  "authors": [
    "C. M. Mynhardt",
    "L. Neilson"
  ],
  "comment": "22 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A broadcast on a nontrivial connected graph G with vertex set V is a function f from V to {0,1,...,diam(G)} such that f(v) is at most the eccentricity of v for all vertices v. The weight of f is the sum of the function values taken over V. A vertex u hears f from v if f(v) is positive and d(u,v) is at most f(v). A broadcast f is boundary independent if, for any vertex w that hears f from vertices v_{1},...,v_{k}, where k is at least 2, d(w,v_{i}) equals f(v_{i}) for each i. The maximum weight of a boundary independent broadcast on G is denoted by {\\alpha}_{bn}(G). We prove a sharp upper bound on {\\alpha}_{bn}(T) for a tree T in terms of its order and number of branch vertices of a certain type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-06T03:19:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69"
    ],
    "keywords": [
      "boundary independence broadcast number",
      "sharp upper bound",
      "function values taken",
      "boundary independent broadcast",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}