Linearly many faults in Cayley graphs generated by transposition trees

Linearly many faults in 2‐tree‐generated networks

“…Moreover, in each of these proofs induction on n is used. So it is natural to use double induction to prove our next result, first on k (strong form), then on n. Note that the proof is similar to the proof of the main result in [10]. Proof.…”

“…Many interconnection networks have been examined in this aspect, when the number of faults is about twice the smallest degree; see [4,5,8,10,21]. One can even go further and ask what happens when more, even linearly many vertices are deleted.…”

“…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.…”

Conditional diagnosability of alternating group networks

“…If S n \F is not connected, then S n \F has two components, one of which has exactly one vertex, or has two vertices with an edge, in which F is the union of the neighbour sets of these two vertices excluding themselves. Cheng and Lipták [22] further generalized this result to star graphs with linearly many faults. Moreover, in terms of the size of connected components, Hsu et al [14] and Lin et al [13] also showed the conditional diagnosabilities for hypercube and star graphs, respectively.…”

Conditional connectivity of Cayley graphs generated by transposition trees

“…vertices, see [9] for the details. The networks based on Cayley graphs generated by transpositions have many advantageous properties, see, for example, [2][3][4]9]. In particular, the star graphs as a network model received much attention, see [2][3][4]8,9,11] for the details.…”