Strong Zero-divisor Graph of p.q.-Baer \(\ast\)-Rings
DOI:
https://doi.org/10.26713/cma.v16i3.3333Keywords:
∗-Ring, p.q.-Baer ∗-ring, Central projections, Zero-divisor graph, Complement of the graphAbstract
In this paper, we study the strong zero-divisor graph of a p.q.-Baer \(\ast\)-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 \(\ast\)-ring contains at least six central projections. The diameter and girth of the complement are determined, and we characterize p.q.-Baer \(\ast\)-rings for which strong zero-divisor graph is complemented.
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