Strong zero-divisor graph of p.q.-Baer $*$-rings
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917746443288576 |
|---|---|
| author | Khairnar, Anil Kumbhar, Nana Waphare, B. N. |
| author_facet | Khairnar, Anil Kumbhar, Nana Waphare, B. N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong zero-divisor graph of p.q.-Baer $*$-rings Khairnar, Anil Kumbhar, Nana Waphare, B. N. Combinatorics 16W10, 05C25, 13A70, 05C15 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. |
| title | Strong zero-divisor graph of p.q.-Baer $*$-rings |
| topic | Combinatorics 16W10, 05C25, 13A70, 05C15 |
| url | https://arxiv.org/abs/2408.05949 |