{
  "id": "2305.12688",
  "version": "v1",
  "published": "2023-05-22T03:53:18.000Z",
  "updated": "2023-05-22T03:53:18.000Z",
  "title": "Testing Isomorphism of Graphs in Polynomial Time",
  "authors": [
    "Rui Xue"
  ],
  "categories": [
    "math.CO",
    "cs.CC",
    "cs.DM"
  ],
  "abstract": "Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is graph-isomorphism complete and that the stable partitions of binding graphs by the Weisfeiler-Lehman (WL) algorithm produce automorphism partitions. To test the isomorphism of two graphs $G$ and $H$, one computes the stable graph of the binding graph $[G\\uplus H]$ for the disjoint union graph $G\\uplus H$. The automorphism partition reveals the isomorphism of $G$ and $H$. Because the WL algorithm is a polynomial-time procedure, the claim can be made that the graph-isomorphism problem is in complexity class $\\mathtt{P}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-22T03:53:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial time",
      "testing isomorphism",
      "binding graph",
      "algorithm produce automorphism partitions",
      "disjoint union graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}