{
  "id": "2406.15822",
  "version": "v1",
  "published": "2024-06-22T11:43:05.000Z",
  "updated": "2024-06-22T11:43:05.000Z",
  "title": "On the Weisfeiler-Leman dimension of circulant graphs",
  "authors": [
    "Yulai Wu",
    "Ilia Ponomarenko"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A circulant graph is a Cayley graph of a finite cyclic group. The Weisfeiler-Leman-dimension of a circulant graph $X$ with respect to the class of all circulant graphs is the smallest positive integer~$m$ such that the $m$-dimensional Weisfeiler-Leman algorithm correctly tests the isomorphism between $X$ and any other circulant graph. It is proved that for a circulant graph of order $n$ this dimension is less than or equal to $\\Omega(n)+3$, where $\\Omega(n)$ is the number of prime divisors of~$n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-22T11:43:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05C60",
      "05E18",
      "F.2.2"
    ],
    "keywords": [
      "circulant graph",
      "weisfeiler-leman dimension",
      "dimensional weisfeiler-leman algorithm correctly tests",
      "finite cyclic group",
      "cayley graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}