{
  "id": "1108.5949",
  "version": "v1",
  "published": "2011-08-30T12:54:07.000Z",
  "updated": "2011-08-30T12:54:07.000Z",
  "title": "Equality in a Linear Vizing-Like Relation that Relates the Size and Total Domination Number of a Graph",
  "authors": [
    "Michael A. Henning",
    "Ernst J. Joubert"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph each component of which has order at least 3, and let $G$ have order $n$, size $m$, total domination number $\\gamma_t$ and maximum degree $\\Delta(G)$. Let $\\Delta = 3$ if $\\Delta(G) = 2$ and $\\Delta = \\Delta (G)$ if $\\Delta(G) \\ge 3$. It is known [J. Graph Theory 49 (2005), 285--290; J. Graph Theory 54 (2007), 350--353] that $m \\le \\Delta (n- \\gamma_t)$. In this paper we characterize the extremal graphs $G$ satisfying $m = \\Delta (n- \\gamma_t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-30T12:54:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69"
    ],
    "keywords": [
      "total domination number",
      "linear vizing-like relation",
      "graph theory",
      "extremal graphs",
      "maximum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5949H"
    }
  }
}