{
  "id": "1410.1169",
  "version": "v1",
  "published": "2014-10-05T15:55:34.000Z",
  "updated": "2014-10-05T15:55:34.000Z",
  "title": "On the $n-$dominating graph of $K_{n}$",
  "authors": [
    "Saeid Alikhani",
    "Davood Fatehi"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a graph. A set $S\\subseteq V(G)$ is a dominating set, if every vertex in $V(G)\\backslash S$ is adjacent to at least one vertex in $S$. The $k$-dominating graph of $G$, $D_k (G)$, is defined to be the graph whose vertices correspond to the dominating sets of $G$ that have cardinality at most $k$. Two vertices in $D_k(G)$ are adjacent if and only if the corresponding dominating sets of $G$ differ by either adding or deleting a single vertex. In this paper we consider $D_n(K_n)$ and study some of its properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-05T15:55:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C60",
      "05C69"
    ],
    "keywords": [
      "dominating graph",
      "vertices correspond",
      "single vertex",
      "corresponding dominating sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.1169A"
    }
  }
}