{
  "id": "1612.03579",
  "version": "v1",
  "published": "2016-12-12T09:21:41.000Z",
  "updated": "2016-12-12T09:21:41.000Z",
  "title": "Enumerating Cayley (di-)graphs on dihedral groups",
  "authors": [
    "Xueyi Huang",
    "Qiongxiang Huang"
  ],
  "comment": "14 pages, 0 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $p$ be an odd prime, and $D_{2p}=\\langle \\tau,\\sigma\\mid \\tau^p=\\sigma^2=e,\\sigma\\tau\\sigma=\\tau^{-1}\\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to isomorphism by using the P\\'{o}lya enumeration theorem. In the process, we also enumerate (connected) Cayley digraphs on $D_{2p}$ of out-degree $k$ up to isomorphism for each $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T09:21:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "dihedral group",
      "enumerating cayley",
      "odd prime",
      "isomorphism",
      "enumeration theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}