Abstract
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 Sn,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 Sn,k is n−2, that is, there exist (n−2) internally disjoint trees connecting x,y,z and w in Sn,k for four arbitrary vertices x,y,z and w of Sn,k. Two known results about the 3-set tree connectivity of star graphs and (n,k)-star graphs are immediate consequences of our result.
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