{
  "id": "2212.12900",
  "version": "v1",
  "published": "2022-12-25T13:19:29.000Z",
  "updated": "2022-12-25T13:19:29.000Z",
  "title": "Characterization of rings with genus two cozero-divisor graphs",
  "authors": [
    "Praveen Mathil",
    "Barkha Baloda",
    "Jitender Kumar"
  ],
  "comment": "16 Figures",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$ is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $x \\notin Ry$ and $y \\notin Rx$. The reduced cozero-divisor graph of a ring $R$, is an undirected simple graph whose vertex set is the set of all nontrivial principal ideals of $R$ and two distinct vertices $(a)$ and $(b)$ are adjacent if and only if $(a) \\not\\subset (b)$ and $(b) \\not\\subset (a)$. In this paper, we characterize all classes of finite non-local commutative rings for which the cozero-divisor graph and reduced cozero-divisor graph is of genus two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-25T13:19:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "undirected simple graph",
      "reduced cozero-divisor graph",
      "characterization",
      "distinct vertices",
      "nontrivial principal ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}