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

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 P_m ◦ W_n, which represents the lexicographic product of a wheel and a path. Under the PMC model, we prove that the diagnosability of P_m ◦ W_n 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 P_m ◦ W_n exhibits strong fault diagnosis capabilities. Furthermore, the lexicographic product offers a promising approach to designing interconnection network architectures for large-scale multiprocessor systems.