{
  "id": "2101.04397",
  "version": "v1",
  "published": "2021-01-12T10:39:35.000Z",
  "updated": "2021-01-12T10:39:35.000Z",
  "title": "On the number of isolate dominating sets of certain graphs",
  "authors": [
    "Nima Ghanbari",
    "Saeid Alikhani"
  ],
  "comment": "12 pages, 4 figures, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $S\\subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$. The cardinality of a smallest dominating set of $G$, denoted by $\\gamma(G)$, is the domination number of $G$. A dominating set $S$ is an isolate dominating set of $G$, if the induced subgraph $G[S]$ has at least one isolated vertex. The isolate domination number, $\\gamma_0(G)$, is the minimum cardinality of an isolate dominating set of $G$. In this paper, we count the number of isolate dominating sets of some specific graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T10:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "isolate dominating set",
      "isolate domination number",
      "simple graph",
      "specific graphs",
      "minimum cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}