Constructing vertex-disjoint paths in (n, k)-star graphs

This work develops a novel general routing algorithm, which is a routing function, for constructing a container of width n 1 between any pair of vertices in an (n, k)-star graph with connectivity n 1. Since the wide diameters in an (n, n 1)-star graph and an (n, 1)-star graph have been derived by Lin et al. (2004), this work only addresses an (n, k)-star with 2 k n 2. The length of the longest container among all constructed containers serves as the upper bound of the wide diameter of an (n, k)-star graph. Moreover, this study also describes a lower bound of the wide diameter of an (n, k)-star graph with 2 k n 2 , and a lower bound of the wide diameter of a regular graph with connectivity 2. The measurement results demonstrate that the wide diameter of an (n, k)-star graph is its diameter plus 2 for 2 k n 2 , or between its diameter plus 1 and plus 2 for n 2 +1 k n+2.