Menu
The maximum number of internal disjoint paths between any two distinct nodes of faulty enhanced hypercube \( Q_{n,k} (1 \leq k \leq n-1) \) are considered in a more flexible approach. Using the structural properties of \( Q_{n,k} (1 \leq k \leq n-1) \), \( \min(d_{Q_{n,k}-V}(x), d_{Q_{n,k}-V}(y)) \) disjoint paths connecting two distinct vertices \( x \) and \( y \) in an \( n \)-dimensional faulty enhanced hypercube \( Q_{n,k}-V (n \geq 8, k \neq n-2, n-1) \) are conformed when \( |V’| \) is at most \( n-1 \). Meanwhile, it is proved that there exists \( \min(d_{Q_{n,k}-V}(x), d_{Q_{n,k}-V}(y)) \) internal disjoint paths between \( x \) and \( y \) in \( Q_{n,k}-V (n \geq 8, k \neq n-2, n-1) \), under the constraints that (1) The number of faulty vertices is no more than \( 2n-3 \); (2) Every vertex in \( Q_{n,k}-V’ \) is incident to at least two fault-free vertices. This results generalize the results of the faulted hypercube \( FQ_n \), which is a special case of \( Q_{n,k} \), and have improved the theoretical evidence of the fact that \( Q_{n,k} \) has excellent node-fault-tolerance when used as a topology of large-scale computer networks, thus remarkably improving the performance of the interconnect networks.