{
  "id": "1109.2174",
  "version": "v1",
  "published": "2011-09-09T23:28:34.000Z",
  "updated": "2011-09-09T23:28:34.000Z",
  "title": "A Note on Total and Paired Domination of Cartesian Product Graphs",
  "authors": [
    "K. Choudhary",
    "S. Margulies",
    "I. V. Hicks"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A dominating set $D$ for a graph $G$ is a subset of $V(G)$ such that any vertex not in $D$ has at least one neighbor in $D$. The domination number $\\gamma(G)$ is the size of a minimum dominating set in $G$. Vizing's conjecture from 1968 states that for the Cartesian product of graphs $G$ and $H$, $\\gamma(G) \\gamma(H) \\leq \\gamma(G \\Box H)$, and Clark and Suen (2000) proved that $\\gamma(G) \\gamma(H) \\leq 2\\gamma(G \\Box H)$. In this paper, we modify the approach of Clark and Suen to prove a variety of similar bounds related to total and paired domination, and also extend these bounds to the $n$-Cartesian product of graphs $A^1$ through $A^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-09T23:28:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian product graphs",
      "paired domination",
      "domination number",
      "minimum dominating set",
      "vizings conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2174C"
    }
  }
}