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

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 S n , 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 , k is n − 2 , that is, there exist ( n − 2 ) internally disjoint trees connecting x , y , z and w in S n , k for four arbitrary vertices x , y , z and w of S n , 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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