The Diagnosability of Interconnection Networks with Missing Edges and Broken-Down Nodes Under the PMC and MM* Models

Diagnosability is often considered as an important factor for measuring the self-diagnostic ability of network systems. However, classic system-level diagnosis focuses only on processor faults and ignores the objective reality of communication faults. Under real circumstances, missing edges and node failures usually occur simultaneously in multiprocessor systems (called hybrid fault circumstances). Therefore, it is important to study the diagnosability of multiprocessor systems under hybrid fault circumstances. In this paper, we propose several diagnosabilities of interconnection networks with missing edges and faulty nodes. By exploring some important relationships between diagnosability and the minimum degree of a network under hybrid fault circumstances, we present and prove the diagnosability of several classic interconnection networks, including BC (bijective connection) networks, star graphs, folded hypercubes, exchanged hypercubes, exchanged crossed cubes, k-ary n-cubes, bubble-sort star graphs and balanced hypercubes, with missing edges and broken-down nodes under the PMC (Preparata, Metze and Chien) and MM* (Maeng and Malek) models.