Structure connectivity of data center networks

Last decade, numerous giant data center networks are built to provide increasingly fashionable web applications. For two integers m≥0 and n≥2, the m-dimensional DCell network with n-port switches Dm,n n-dimensional BCDC Bn have been proposed. As a generalization of connectivity, structure (substructure) connectivity was recently Let G H be connected graphs. F set whose elements subgraphs G, every member is isomorphic (resp. subgraph H). Then H-structure κ(G;H) H-substructure κs(G;H)) size smallest such that G−F disconnected or singleton. it meaningful calculate on some common structures, as star K1,t, path Pk, cycle Ck, complete graph Ks so on. In this paper, we obtain κ(Dm,n;K1,t)=κs(Dm,n;K1,t)=⌈n−11+t⌉+m for 1≤t≤m+n−2 κ(Dm,n;Ks)=⌈n−1s⌉+m 3≤s≤n−1 by analyzing structural properties Dm,n. We also compute κ(Bn;H) κs(Bn;H) H∈{K1,t,Pk,Ck|1≤t≤2n−3,6≤k≤2n−1} n≥5 using g-extra Bn.