{
  "id": "2011.10544",
  "version": "v1",
  "published": "2020-11-20T18:32:13.000Z",
  "updated": "2020-11-20T18:32:13.000Z",
  "title": "On Intersection Graph of Dihedral Group",
  "authors": [
    "Sanhan Khasraw"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\\cap K \\neq \\{e\\}$, where $e$ is the identity of the group $G$. In this paper, we investigate some properties and exploring some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gutman and eccentric connectivity indices of the intersection graph of $D_{2n}$ for $n=p^2$, $p$ is prime. We also find the metric dimension and the resolving polynomial of the intersection graph of $D_{2p^2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-20T18:32:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intersection graph",
      "dihedral group",
      "proper non-trivial subgroups",
      "eccentric connectivity indices",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}