Local diagnosability of bipartite graphs with conditional faulty edges under Preparata, Metze and Chien?s model

Diagnosability of a multiprocessor system is an important research topic. The system or interconnection network has an underlying topology, which usually presented by a graph. In this paper, let G be a bipartite graph with delta(G) = delta and let there be at most two common neighbor vertices of any two vertices in G under the PMC model. We firstly study the diagnosability of G. We prove that G - F keeps the strong local diagnosability property even if it has the set F of (delta-2) faulty edges. Secondly, we study the diagnosability of G with conditional faulty edges. We prove that G - F keeps strong local diagnosability property even if it has the set F of (3 delta - 7) faulty edges, provided that each vertex of G - F is incident with at least two fault-free edges. Finally, we prove that G - F keeps strong local diagnosability property no matter how many edges are faulty, provided that each vertex of G - F is incident with at least three fault-free edges.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper explores the diagnosability of a multiprocessor system based on a bipartite graph, considering both unconditional and conditional faulty edges. The study highlights the importance of maintaining strong local diagnosability properties under various fault scenarios.