{
  "id": "1507.05874",
  "version": "v1",
  "published": "2015-07-21T15:27:24.000Z",
  "updated": "2015-07-21T15:27:24.000Z",
  "title": "The Center and Radius of the Regular Graph of Ideals",
  "authors": [
    "Farzad Shaveisi"
  ],
  "comment": "15 pages, 0 figures",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "The regular graph of ideals of the commutative ring $R$, denoted by ${\\Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is proved that the radius of $\\Gamma_{reg}(R)$ equals $3$. The central vertices of $\\Gamma_{reg}(R)$ are determined, too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-21T15:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C69",
      "13E05",
      "16P20"
    ],
    "keywords": [
      "regular graph",
      "regular element",
      "central vertices",
      "vertex set",
      "distinct vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}