{
  "id": "1307.2175",
  "version": "v2",
  "published": "2013-07-05T15:16:08.000Z",
  "updated": "2013-08-23T20:02:35.000Z",
  "title": "Finite groups whose prime graphs are regular",
  "authors": [
    "Hung P. Tong-Viet"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR",
    "math.CO",
    "math.RT"
  ],
  "abstract": "Let G be a finite group and let Irr(G) be the set of all irreducible complex characters of G. Let cd(G) be the set of all character degrees of G and denote by \\rho(G) the set of primes which divide some character degrees of G. The prime graph \\Delta(G) associated to G is a graph whose vertex set is \\rho(G) and there is an edge between two distinct primes p and q if and only if the product pq divides some character degree of G. In this paper, we show that the prime graph \\Delta(G) of a finite group G is 3-regular if and only if it is a complete graph with four vertices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-23T20:02:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "05C25"
    ],
    "keywords": [
      "finite group",
      "prime graph",
      "character degree",
      "product pq divides",
      "distinct primes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.2175T"
    }
  }
}