{
  "id": "2408.05949",
  "version": "v1",
  "published": "2024-08-12T06:55:07.000Z",
  "updated": "2024-08-12T06:55:07.000Z",
  "title": "Strong zero-divisor graph of p.q.-Baer $*$-rings",
  "authors": [
    "Anil Khairnar",
    "Nana Kumbhar",
    "B. N. Waphare"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the strong zero-divisor graph of a p.q.-Baer $*$-ring. We determine the condition on a p.q.-Baer $*$-ring (in terms of the smallest central projection in a lattice of central projections of a $*$-ring), so that its strong zero-divisor graph contains a cut vertex. It is proved that the set of cut vertices of a strong zero-divisor graph of a p.q.-Baer $*$-ring forms a complete subgraph. We prove that the complement of the strong zero-divisor graph of a p.q.-Baer $*$-ring is connected if and only if the $*$-ring contains at least six central projections. We characterize the diameter and girth of the complement of a strong zero-divisor graph of a p.q.-Baer $*$-ring. Also, we characterize p.q.-Baer $*$-rings whose strong zero-divisor graph is complemented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-12T06:55:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16W10",
      "05C25",
      "13A70",
      "05C15"
    ],
    "keywords": [
      "cut vertex",
      "strong zero-divisor graph contains",
      "smallest central projection",
      "complete subgraph",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}