Strong zero-divisor graph of p.q.-Baer $*$-rings

Authors

  • NANA KUMBHAR BVDU, Yashwantrao Mohite College, Pune-411038
  • Anil Khairnar Department of Mathematics, MES Abasaheb Garware College, Pune, 411004, Maharashtra, India https://orcid.org/0000-0003-2187-6362
  • B. N. Waphare Department of Mathematics, Savitribai Phule Pune University, Pune-411007, Maharashtra, India https://orcid.org/0000-0002-0693-6067

Keywords:

$*$-ring, p.q.-Baer $*$-ring, central projections, zero-divisor graph, complement of the graph

Abstract

In this paper, we study the strong zero-divisor graph of a p.q.-Baer $*$-ring and establish conditions, based on the smallest central projection in the lattice of central projections, under which the graph contains a cut vertex. We prove that the set of cut vertices forms a complete subgraph. Furthermore, we show that the complement of this graph is connected if and only if the $*$-ring contains at least six central projections. The diameter and girth of the complement are determined, and we characterize p.q.-Baer $*$-rings whose strong zero-divisor graph is complemented.

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Published

19-02-2026

How to Cite

KUMBHAR, N., Khairnar, A., & Waphare, B. N. (2026). Strong zero-divisor graph of p.q.-Baer $*$-rings. Communications in Mathematics and Applications, 16(3). Retrieved from https://www.rgnpublications.com/journals/index.php/cma/article/view/3333

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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