Diagnosability of the lexicographic product of paths and stars under PMC model

Multiprocessor systems provide significant computational power for modern society, supporting technological advancements and innovations across various industries and fields. In the design and maintenance of such systems, the network’s diagnosability is a crucial parameter. It measures the system’s capability to diagnose and identify faulty processors, thereby directly affecting the system’s reliability, security, and performance. This paper studies a network structure P<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf>○S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> which is based on the lexicographic product of paths and stars. Utilizing the PMC model to analyze this network structure, it is found that its diagnosability is 2 + n. Furthermore, when 0 ≤ h < 2 + n, its h-edge tolerable diagnosability is 2 + n−h.