Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model.
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| Title: | Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model. |
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| Authors: | Bu Chen1 achenbu@163.com, Feng Li2 li2006369@126.com |
| Source: | IAENG International Journal of Applied Mathematics. Jun2025, Vol. 55 Issue 6, p1782-1788. 7p. |
| Subjects: | Fault diagnosis, Multiprocessors, Wheels |
| Abstract: | Diagnosability is a critical metric for evaluating the fault diagnosis capabilities of interconnection networks in multiprocessor systems. Accurate assessment of diagnosability requires system-level fault diagnosis models, which play a key role in the design of new interconnection networks. In this paper, we introduce a novel network, denoted as Pm ◦ Wn, which represents the lexicographic product of a wheel and a path. Under the PMC model, we prove that the diagnosability of Pm ◦ Wn is 3 + n and its h-edge tolerable diagnosability is 3 + n - h for 0 ≤ h < 3 + n, m ≥ 4, and n ≥ 7. These results reveal that Pm ◦Wn exhibits strong fault diagnosis capabilities. Furthermore, the lexicographic product offers a promising approach to designing interconnection network architectures for large-scale multiprocessor systems. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 185633659 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bu+Chen%22">Bu Chen</searchLink><relatesTo>1</relatesTo><i> achenbu@163.com</i><br /><searchLink fieldCode="AR" term="%22Feng+Li%22">Feng Li</searchLink><relatesTo>2</relatesTo><i> li2006369@126.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jun2025, Vol. 55 Issue 6, p1782-1788. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fault+diagnosis%22">Fault diagnosis</searchLink><br /><searchLink fieldCode="DE" term="%22Multiprocessors%22">Multiprocessors</searchLink><br /><searchLink fieldCode="DE" term="%22Wheels%22">Wheels</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Diagnosability is a critical metric for evaluating the fault diagnosis capabilities of interconnection networks in multiprocessor systems. Accurate assessment of diagnosability requires system-level fault diagnosis models, which play a key role in the design of new interconnection networks. In this paper, we introduce a novel network, denoted as Pm ◦ Wn, which represents the lexicographic product of a wheel and a path. Under the PMC model, we prove that the diagnosability of Pm ◦ Wn is 3 + n and its h-edge tolerable diagnosability is 3 + n - h for 0 ≤ h < 3 + n, m ≥ 4, and n ≥ 7. These results reveal that Pm ◦Wn exhibits strong fault diagnosis capabilities. Furthermore, the lexicographic product offers a promising approach to designing interconnection network architectures for large-scale multiprocessor systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 1782 Subjects: – SubjectFull: Fault diagnosis Type: general – SubjectFull: Multiprocessors Type: general – SubjectFull: Wheels Type: general Titles: – TitleFull: Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bu Chen – PersonEntity: Name: NameFull: Feng Li IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 55 – Type: issue Value: 6 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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