Strong zero-divisor graph of p.q.-Baer $*$-rings
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.
Cite
@article{arxiv.2408.05949,
title = {Strong zero-divisor graph of p.q.-Baer $*$-rings},
author = {Anil Khairnar and Nana Kumbhar and B. N. Waphare},
journal= {arXiv preprint arXiv:2408.05949},
year = {2024}
}