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

Abstract

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 δ ( G ) = δ 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 ( δ − 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 δ − 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.