{
  "id": "1205.0102",
  "version": "v1",
  "published": "2012-05-01T07:24:38.000Z",
  "updated": "2012-05-01T07:24:38.000Z",
  "title": "The p-Domination Number of Complete Multipartite Graphs",
  "authors": [
    "You Lu",
    "Jun-Ming Xu"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a graph and $p$ a positive integer. A subset $S\\subseteq V$ is called a $p$-dominating set of $G$ if every vertex not in $S$ has at least $p$ neighbors in $S$. The $p$-domination number is the minimum cardinality of a $p$-dominating set in $G$. In this paper, we establish an exact formula of the $p$-domination number of all complete multipartite graphs for arbitrary positive integer $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-01T07:24:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69"
    ],
    "keywords": [
      "complete multipartite graphs",
      "p-domination number",
      "dominating set",
      "arbitrary positive integer",
      "minimum cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0102L"
    }
  }
}