{
  "id": "1711.01058",
  "version": "v1",
  "published": "2017-11-03T08:29:10.000Z",
  "updated": "2017-11-03T08:29:10.000Z",
  "title": "Divisor graph of complement of Gamma(R)",
  "authors": [
    "Ravindra Kumar",
    "Om Prakash"
  ],
  "comment": "Communicated to a Journal",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let overline{\\Gamma(R)} be the complement of zero divisor graph of a finite commutative ring R. In this article, we have provided the answer of the question (ii) raised by Osba and Alkam in their paper and prove that overline{\\Gamma(R)} is a divisor graph if R is a local ring. It is shown that when R is a product of two local rings, then overline{\\Gamma(R)} is a divisor graph if one of them is an integral domain. Also, we prove that if cardinality of Ass(R) = 2, then overline{\\Gamma(R)} is a divisor graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-03T08:29:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C25",
      "05C78"
    ],
    "keywords": [
      "complement",
      "zero divisor graph",
      "local ring",
      "integral domain",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}