{
  "id": "2406.04045",
  "version": "v1",
  "published": "2024-06-06T13:15:07.000Z",
  "updated": "2024-06-06T13:15:07.000Z",
  "title": "On the Diameter of Undirected Cayley Graphs of Finite Abelian Groups",
  "authors": [
    "Bela Bajnok",
    "W. Kyle Beatty"
  ],
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT"
  ],
  "abstract": "Let $s$ be a positive integer. Our goal is to find all finite abelian groups $G$ that contain a $2$-subset $A$ for which the undirected Cayley graph $\\Gamma(G,A)$ has diameter at most $s$. We provide a complete answer when $G$ is cyclic, and a conjecture and some partial answers when $G$ is noncyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-06T13:15:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13"
    ],
    "keywords": [
      "finite abelian groups",
      "undirected cayley graph",
      "complete answer",
      "partial answers",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}