{
  "id": "0908.3305",
  "version": "v1",
  "published": "2009-08-23T14:40:08.000Z",
  "updated": "2009-08-23T14:40:08.000Z",
  "title": "Cycles are determined by their domination polynomials",
  "authors": [
    "Saieed Akbari",
    "Mohammad Reza Oboudi"
  ],
  "comment": "To appear in Ars Combinatoria",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a simple graph of order $n$. A dominating set of $G$ is a set $S$ of vertices of $G$ so that every vertex of $G$ is either in $S$ or adjacent to a vertex in $S$. The domination polynomial of $G$ is the polynomial $D(G,x)=\\sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. In this paper we show that cycles are determined by their domination polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-23T14:40:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C38",
      "05C69"
    ],
    "keywords": [
      "domination polynomial",
      "dominating set",
      "simple graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3305A"
    }
  }
}