On the maximal connected component of a hypercube with faulty vertices III

Abstract

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Linearly many faults in 2‐tree‐generated networks

“…One can even go further and ask what happens when more, even linearly many vertices are deleted. This was examined for the hypercube in [22] and for certain Cayley graphs generated by transpositions in [10], and it was shown that the resulting network will have a large component containing almost all vertices.…”

A (4n−9)/3 diagnosis algorithm on n-dimensional cube network

“…[21][22][23][24][25], it is possible to design efficient t/k diagnosis algorithm on hypercube in respect to k P 4. The method developed in this work should be extended to design t/k diagnosis algorithms on other types of interconnection networks such as star network [1], circulant network [2], folded hypercube [4], crossed cube [6], hierarchical cubic network [9], supercube [15] and twisted cube [19], to name a few.…”

Conditional fault diagnosis of hierarchical hypercubes

“…Yang et al [28][29][30] proved that the hypercube Q n with f faulty processors has a component of size at least 2 n − f − 1 if f ≤ 2n − 3, and size at least 2 n − f − 2 if f ≤ 3n − 6. Recently, Yang and Meng [27] determined the extra connectivity of hypercubes, Hsu et al [12] went further to establish the component connectivity of hypercubes.…”

“…One can even go further and ask what happens when more vertices are deleted. This has been examined for the hypercube in [28][29][30] and for certain Cayley graphs generated by transpositions in [5], and it has been shown that the surviving network has a large component containing almost all vertices.…”