The 4-set tree connectivity of (, )-star networks.

The tree connectivity, as a generalization of the traditional connectivity, can serve to measure the capability of connection for vertices in a network. The (n, k)-star graph S-n,S-k can be used to model the topological structure of a large-scale parallel processing system. We show in this article that the 4-set tree connectivity of S-n,S-k is n - 2, that is, there exist (n - 2) internally disjoint trees connecting x, y, z and w in S-n,S-k for four arbitrary vertices x, y, z and w of S-n,S-k. Two known results about the 3-set tree connectivity of star graphs and (n, k)-star graphs are immediate consequences of our result. (C) 2020 Elsevier B.V. All rights reserved.