Topological Properties on the Wide and Fault Diameters of Exchanged Hypercubes

The n-dimensional hypercube is one of the most popular topological structure for interconnection networks in parallel computing and communication systems. The exchanged hypercube EH(s, t), a variant of the hypercube, retains several valuable and desirable properties of the hypercube such as a small diameter, bipancyclicity, and super connectivity. In this paper, we construct s + 1 (or t + 1) internally vertex-disjoint paths between any two vertices for parallel routes in the exchanged hypercube EH(s, t) for 3 ≤ s ≤ t. We also show that both the (s + 1)-wide diameter and s-fault diameter of the exchanged hypercube EH(s, t) are s + t + 3 for 3 ≤ s ≤ t.