The Local Diagnosability of a Class of Cayley Graphs with Conditional Faulty Edges Under the PMC Model

The diagnosability of a multiprocessor system is of great significance in measuring the reliability and faulty tolerance of interconnection networks. In this paper, we firstly study the diagnosability of a class of Cayley graphs Cay(H-n, S-n) under the PMC model. We prove that Cay(H-n, S-n) - F keeps the strong local diagnosability property even if it has the set F of (m - 2) faulty edges and m - 2 is maximum number of faulty edges, where m is the regular degree of Cay(H-n, S-n). Secondly, we study the diagnosability of Cay(H-n, S-n) with conditional faulty edges under the PMC model. We prove that Cay(H-n, S-n) - F keeps strong local diagnosability property even if it has the set F of (3m - 10) faulty edges, provided that each vertex of Cay(H-n, S-n) - F is incident with at least two fault-free edges, where 3m - 10 is maximum number of faulty edges. Finally, we prove that Cay(H-n, S-n)- F keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of Cay(H-n, S-n)- F is incident with at least four fault-free edges.

Automated summary

In this paper, we investigate the diagnosability of a class of Cayley graphs under the PMC model. We prove that even with a certain number of faulty edges, the graphs still maintain strong local diagnosability property. Additionally, we demonstrate that as long as each vertex is incident with a sufficient number of fault-free edges, the graphs maintain strong local diagnosability, regardless of the number of faulty edges.