{
  "id": "1511.04884",
  "version": "v1",
  "published": "2015-11-16T09:46:24.000Z",
  "updated": "2015-11-16T09:46:24.000Z",
  "title": "On the global offensive alliance in unicycle graphs",
  "authors": [
    "Mohamed Bouzefrane",
    "Saliha Ouatiki"
  ],
  "comment": "11 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G=(V,E)$, a set $S\\subseteq V$ is a dominating set if every vertex in $V-S$ has at least a neighbor in $S$. A dominating set $S$ is a global offensive alliance if for each vertex $v$ in $V-S$ at least half the vertices from the closed neighborhood of $v$ are in $S.$ The domination number $\\gamma(G)$ is the minimum cardinality of a dominating set of $G$, and the global offensive alliance number $\\gamma_{o}(G)$ is the minimum cardinality of a global offensive alliance of $G$. We show that if $G$ is a connected unicycle graph of order $n$ with $l(G)$ leaves and $s(G)$ support vertices then $\\gamma_{o}(G)\\geq\\frac{n-l(G)+s(G)}{3}$. Moreover, we characterize all extremal unicycle graphs attaining this bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-16T09:46:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C75",
      "G.2.2",
      "F.2.2"
    ],
    "keywords": [
      "dominating set",
      "minimum cardinality",
      "global offensive alliance number",
      "extremal unicycle graphs attaining",
      "connected unicycle graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151104884B"
    }
  }
}