On the maximal connected component of hypercube with faulty vertices

Conditional diagnosability of alternating group networks

“…Therefore, in evaluating a distributed system, it is necessary to estimate the size of the maximal connected component of the underlying network when the system begins to lose processors. Yang et al [19] proved that the hypercube of size n with a set F of at most 2n − 3 failed processors has a connected component of size 2 n − |F | − 1, and that it has a connected component of size 2 n − |F | − 2 if |F | 3n − 6. Similar result on a star graph S n was also obtained by Yang et al [20].…”

Linearly many faults in 2‐tree‐generated networks

“…When the number of faults is the smallest degree, a new concept of connectivity is necessary, since the graph may become disconnected. Thus several types of superconnectivity were introduced and examined for various classes of graphs in [4,7,9,11,12,16,20], including superconnectedness and tightly superconnectedness, where only singletons can appear in the remaining network, and restricted connectivity, where each remaining component must have a certain minimum size.…”

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.…”