Strong Zero-divisor Graph of p.q.-Baer \(*\)-Rings - Kumbhar, Nana; Khairnar, Anil; Waphare, B. N. (Communications in Mathematics and Applications, 2025)
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 for which strong zero-divisor graph is complemented.