{
  "id": "1609.05854",
  "version": "v1",
  "published": "2016-09-19T18:44:46.000Z",
  "updated": "2016-09-19T18:44:46.000Z",
  "title": "Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs",
  "authors": [
    "Aras Erzurumluoglu",
    "David Pike",
    "Karen Meagher"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we compare the brushing number of a graph with the zero-forcing number of its line graph. We prove that the zero-forcing number of the line graph is an upper bound for the brushing number by constructing a brush configuration based on a zero-forcing set for the line graph. Using a similar construction, we also prove the conjecture that the zero-forcing number of a graph is no more than the zero-forcing number of its line graph; moreover we prove that the brushing number of a graph is no more than the brushing number of its line graph. All three bounds are shown to be tight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-19T18:44:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C85",
      "05C57"
    ],
    "keywords": [
      "line graph",
      "brushing number",
      "zero-forcing number",
      "brush configuration",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}