{
  "id": "1204.4514",
  "version": "v1",
  "published": "2012-04-20T01:50:58.000Z",
  "updated": "2012-04-20T01:50:58.000Z",
  "title": "The 2-Domination and 2-Bondage Numbers of Grid Graphs",
  "authors": [
    "You Lu",
    "Jun-Ming Xu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $p$ be a positive integer and $G=(V,E)$ be a simple graph. A subset $D\\subseteq V$ is a $p$-dominating set if each vertex not in $D$ has at least $p$ neighbors in $D$. The $p$-domination number $\\g_p(G)$ is the minimum cardinality among all $p$-dominating sets of $G$. The $p$-bondage number $b_p(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with a $p$-domination number greater than the $p$-domination number of $G$. In this note we determine the 2-domination number $\\g_2$ and 2-bondage number $b_2$ for the grid graphs $G_{m,n}=P_m\\times P_n$ for $2\\leq m\\leq 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-20T01:50:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grid graphs",
      "dominating set",
      "domination number greater",
      "simple graph",
      "minimum cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4514L"
    }
  }
}