The Diagnosability of the Generalized Cartesian Product of Networks
Abstract
:1. Introduction
2. Preliminaries
2.1. Definitions and Notations
2.2. The PMC Model
2.3. The MM Model
2.4. Local Diagnosis
2.5. The Generalized Cartesian Product of Networks
- When all ’s are isomorphic to G and M is the canonical perfect matching then is the classical Cartesian product of G and H;
- If H is isomorphic to , then is the Matching Composition Network (MCN), where is the complete network with two vertices;
- If H is isomorphic to , then is the Cycle Composition Network (CCN), where is the cycle with m vertices;
- We give an example to show that for the same and H, once the perfect matching is different then we obtain different networks. See Figure 3 for an illustration. In the following, we always use blue lines to represent the edges in and red lines to represent the edges in the perfect matching M.
3. The Diagnosability of the GCPNs under the PMC Model
4. The Diagnosability of the GCPNs under the MM Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Chen, M.; Lin, C.-K. The Diagnosability of the Generalized Cartesian Product of Networks. Mathematics 2023, 11, 2615. https://doi.org/10.3390/math11122615
Chen M, Lin C-K. The Diagnosability of the Generalized Cartesian Product of Networks. Mathematics. 2023; 11(12):2615. https://doi.org/10.3390/math11122615
Chicago/Turabian StyleChen, Meirun, and Cheng-Kuan Lin. 2023. "The Diagnosability of the Generalized Cartesian Product of Networks" Mathematics 11, no. 12: 2615. https://doi.org/10.3390/math11122615
APA StyleChen, M., & Lin, C.-K. (2023). The Diagnosability of the Generalized Cartesian Product of Networks. Mathematics, 11(12), 2615. https://doi.org/10.3390/math11122615