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The Generalized Connectivity of Data Center Networks

    The generalized k-connectivity of a graph G is a parameter that can measure the reliability of a network G to connect any k vertices in G, which is a generalization of traditional connectivity. Let SV(G) and κG(S) denote the maximum number r of edge-disjoint trees T1,T2,,Tr in G such that V(Ti)V(Tj)=S for any i,j{1,2,,r} and ij. For an integer k with 2kn, the generalized k-connectivity of a graph G is defined as κk(G)=min{κG(S)|SV(G) and |S|=k}. Data centers are essential to the business of companies such as Google, Amazon, Facebook and Microsoft et al. Based on data centers, the data center networks Dk,n, introduced by Guo et al. in 2008, have many desirable properties. In this paper, we study the generalized 3-connectivity of Dk,n and show that κ3(Dk,n)=n+k2 for k0 and n3.

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