{
  "id": "2010.05285",
  "version": "v1",
  "published": "2020-10-11T17:11:08.000Z",
  "updated": "2020-10-11T17:11:08.000Z",
  "title": "Stability of Cayley graphs on abelian groups of odd order",
  "authors": [
    "Dave Witte Morris"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $X$ be a connected Cayley graph on an abelian group of odd order, such that no two distinct vertices of $X$ have exactly the same neighbours. We show that the direct product $X \\times K_2$ (also called the \"canonical double cover\" of $X$) has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors $X$ and $K_2$). This means that $X$ is \"stable\". The proof is short and elementary. The theory of direct products implies that $K_2$ can be replaced with members of a much more general family of connected graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-11T17:11:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C76"
    ],
    "keywords": [
      "odd order",
      "abelian group",
      "direct products implies",
      "distinct vertices",
      "connected cayley graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}