Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model.

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Bibliographic Details
Title:	Diagnosability of Lexicographic Product of Wheels and Paths under the PMC Model.
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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978