The spanning connectivity of folded hypercubes☆

Topological Properties on the Wide and Fault Diameters of Exchanged Hypercubes

“…Moreover, this interconnection network has many benefits such as parallel routing and fault tolerance. In recent years, many literature references discuss the topic of internally disjoint paths in some specific networks, such as hypercubes [20], crossed cubes [8], ðn; kÞ-star graphs [12], folded hypercubes [15], hypercubelike graphs [19], hierarchical hypercubes [21], and augmented k-ary n-cubes [22]. Next, we discuss the fault and wide diameters of exchanged hypercubes.…”

“…The fault diameter, which was first proposed in [9], is used to estimate the effects of faults on the diameter, while the wide diameter is used to measure the diameter of the connections with prescribed bandwidths, and it is a combination of both the diameter and connectivity. The fault and wide diameters have been discussed in [2], [3], [4], [6], [12], [15], [21], [22]. In this study, we construct s þ 1 (or t þ 1) internally disjoint paths between any two vertices for parallel routes in the exchanged hypercube EHðs; tÞ for 3 s t. We also prove that both the ðs þ 1Þ-wide diameter and s-fault diameter are s þ t þ 3 for 3 s t.…”

One-to-One Disjoint Path Covers in DCell

“…However, the problem of finding disjoint path covers is NP-complete [13]. Therefore, a large amount researches on problems of disjoint path covers focused on different special networks, such as hypercubes [13][14][15][16], their variants [17][18][19], and others [20][21][22].…”