The h-edge tolerable diagnosability of balanced hypercubes

Abstract

To measure the fault diagnosis capability of a multiprocessor system with faulty links, Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1-8] introduced the h-edge tolerable diagnosability. This kind of diagnosability is a generalization of the concept of traditional diagnosability. In this paper, as complement to the results in [Theoret.Comput. Sci. 760 (2019) 1-14], we completely determine the h-edge tolerable diagnosability of balanced hypercubes BH n under the PMC model and the MM * model. Thus, the traditional diagnosability of BH n is also determined.

Hybrid fault diagnosis capability analysis of regular graphs

“…Recently, Lian et al [6] established the h-edge tolerable diagnosability of a k-regular k-connected graph under the PMC model and the MM * model. Zhang et al [22] determined the h-edge tolerable diagnosabilities of triangle-free graphs under the PMC model and the MM * model, which extends the results of triangle-free regular graphs [20]. Zhang et al [21] determined the h-edge tolerable diagnosabilities of k-regular 2-cn graphs under the PMC model for h ≤ k − 5.…”

“…In 2019, Zhu et al [23] determined the h-edge tolerable diagnosabilities of hypercubes under the PMC model and the MM * model. Wei and Xu [17,20] established the hedge tolerable diagnosabilities of k-regular triangle-free graphs and balanced hypercubes under the PMC model and the MM * model. Recently, Lian et al [6] established the h-edge tolerable diagnosability of a k-regular k-connected graph under the PMC model and the MM * model.…”

“…The MM * model which is the development of the MM model [9], proposed by Sengupta and Dahbura [12], assumes that each processor has to test two processors if the processor is adjacent to the latter two processors. Some references related to fault diagnosis studies under the PMC model or MM * model can be seen in [2,5,6,[13][14][15][16][17][18][19][20][21][22][23].…”

The generalized 4-connectivity of balanced hypercubes

“…Compared with the hypercube, the balanced hypercube not only keeps many good properties like the hypercube but also has other better properties than the hypercube, including the smaller diameter and that each vertex has a paired vertex which has the same neighborhood [19], so each processor has an alternative processor 2 D. Cheng when processes the same adjacent relationship tasks. Balanced hypercube's other properties have received extensive research [3,4,8,[13][14][15][17][18][19][20][21][22][23].…”