{
  "id": "1903.00407",
  "version": "v1",
  "published": "2019-03-01T16:57:50.000Z",
  "updated": "2019-03-01T16:57:50.000Z",
  "title": "On Cayley representations of finite graphs over abelian p-groups",
  "authors": [
    "Grigory Ryabov"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We construct a polynomial-time algorithm which given a graph $\\Gamma$ finds the full set of non-equivalent Cayley representations of $\\Gamma$ over the group $D\\cong C_p\\times C_{p^k}$, where $p\\in\\{2,3\\}$ and $k\\geq 1$. This result implies that the recognition and the isomorphism problems for Cayley graphs over $D$ can be solved in polynomial time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-01T16:57:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite graphs",
      "abelian p-groups",
      "non-equivalent cayley representations",
      "polynomial time",
      "polynomial-time algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}