{
  "id": "1409.4939",
  "version": "v1",
  "published": "2014-09-17T10:41:15.000Z",
  "updated": "2014-09-17T10:41:15.000Z",
  "title": "On finite groups all of whose cubic Cayley graphs are integral",
  "authors": [
    "Xuanlong Ma",
    "Kaishun Wang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "For any positive integer $k$, let $\\mathcal{G}_k$ denote the set of finite groups $G$ such that all Cayley graphs ${\\rm Cay}(G,S)$ are integral whenever $|S|\\le k$. Est${\\rm \\acute{e}}$lyi and Kov${\\rm \\acute{a}}$cs \\cite{EK14} classified $\\mathcal{G}_k$ for each $k\\ge 4$. In this paper, we characterize the finite groups each of whose cubic Cayley graphs is integral. Moreover, the class $\\mathcal{G}_3$ is characterized. As an application, the classification of $\\mathcal{G}_k$ is obtained again, where $k\\ge 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-17T10:41:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C50",
      "20C10"
    ],
    "keywords": [
      "cubic cayley graphs",
      "finite groups",
      "classification",
      "application",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4939M"
    }
  }
}