“…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.…”