{
  "id": "1311.4899",
  "version": "v1",
  "published": "2013-11-19T21:41:19.000Z",
  "updated": "2013-11-19T21:41:19.000Z",
  "title": "Alliances and related parameters in graphs",
  "authors": [
    "Henning Fernau",
    "Juan A. Rodriguez-Velazquez"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we show that several graph parameters are known in different areas under completely different names. More specifically, our observations connect signed domination, monopolies, $\\alpha$-domination, $\\alpha$-independence, positive influence domination, and a parameter associated to fast information propagation in networks to parameters related to various notions of global $r$-alliances in graphs. We also propose a new framework, called (global) $(D,O)$-alliances, not only in order to characterize various known variants of alliance and domination parameters, but also to suggest a unifying framework for the study of alliances and domination. Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-19T21:41:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C85",
      "68Q17"
    ],
    "keywords": [
      "related parameters",
      "fast information propagation",
      "observations connect signed domination",
      "positive influence domination",
      "domination parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4899F"
    }
  }
}