On reliability of the folded hypercubes

Abstract

In this paper, we explore the 2-extra connectivity and 2-extra-edge-connectivity of the folded hypercube FQ n . We show that j 2 (FQ n ) = 3n À 2 for n P 8; and k 2 (FQ n ) = 3n À 1 for n P 5. That is, for n P 8 (resp. n P 5), at least 3n À 2 vertices (resp. 3n À 1 edges) of FQ n are removed to get a disconnected graph that contains no isolated vertices (resp. edges). When the folded hypercube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.

On the connectivity and restricted edge-connectivity of 3-arc graphs

“…Furthermore, a λ (2) -connected graph is said to be λ (2) -optimal if λ (2) = ξ. Recent results on this property are obtained in [2,5,12,13,18,21,23]. Notice that if λ (2) ≤ δ, then λ (2) = λ.…”

Broadcasting secure messages via optimal independent spanning trees in folded hypercubes

“…Ma and Xu [23] proved that FQ n is node-symmetric and edge-symmetric. For more results related to folded hypercubes, the reader can refer to [2,7,12,19,29,36,37].…”

Linear Wirelength of Folded Hypercubes

“…It is easy to see that any r -dimensional folded hypercube F Q r can be viewed as G(0Q r −1 , 1Q r −1 ; C + C) where 0Q r −1 and 1Q r −1 are two (r − 1)-dimensional hypercubes with the prefix 0 and 1 of each vertex, respectively, and C = {(0u, 1u) : 0u ∈ V (0Q r −1 ) and 1u ∈ V (1Q r −1 )}, C = {(0u, 1u) : 0u ∈ V (0Q r −1 ) and 1u ∈ V (1Q r −1 )} [13].…”