The g-Good-Neighbor Conditional Diagnosability of Exchanged Crossed Cube under the MM* Model

Abstract

Diagnosability plays an important role in appraising the reliability and fault tolerance of symmetrical multiprocessor systems. The novel g-good-neighbor conditional diagnosability restrains that every fault-free node contains at least g fault-free neighbors and is suitable for large scale multiprocessor systems, attracting a lot of research attention. The relationships between the g-good-neighbor connectivity and g-good-neighbor diagnosability of graphs under the MM* model are separately studied, but only applicable in regular graphs or just ranges rather than exact values. As a promising network structure, in 2019, Guo et al. obtained that the g-good-neighbor diagnosability of the exchanged crossed cube (ECQ(s,t)) under the PMC model is 2g(s+2−g)−1 (t≥s>g). We noticed that the exact value of the g-good-neighbor diagnosability of ECQ(s,t) under the MM* model is still to be determined. In this paper, by proving the upper and lower bounds of the g-good-neighbor diagnosability of ECQ(s,t), for the first time, we derive that the exact value of its g-good-neighbor diagnosability under the MM* model is tgm(ECQ(s,t))=2g(s+2−g)−1 (t≥s>g), achieving the unity of the g-good-neighbor diagnosability of ECQ(s, t) under both the PMC model and MM* model. Towards the end, simulation experiments are conducted to evaluate the correctness and effectiveness of our conclusion. Our research provides an important supplement to the g-good-neighbor diagnosability of ECQ(s,t).