Structure Fault-tolerance Of Arrangement Graphs And Data Center Networks

The classical connectivity is one of the vital parameters to measure the fault tolerance of a graph.Nevertheless,it is almost impossible for all faulty vertices to be adjacent to a single vertex simultaneously.Therefore,many restricted vertexconnectivities have been proposed.Given a connected graph G and a connected subgraph H of G.The H-structure connectivity ?(G;H)of G is the minimum cardinality of a set of subgraphs F in G,where the elements in F are isomorphic to H,and the deletion of F disconnects G.Similarly,the H-substructure connectivity?s(G;H)of G is the minimum cardinality of a set of subgraphs F in G,where where the elements in F are isomorphic to a connected subgraph of H,and the deletion of F disconnects G.Structure connectivity and substructure connectivity generalize the classical vertex-connectivity.In this paper,we establish ?(An,k;H)and ?s(An,k;H)of the(n,k)-arrangement graph An,k,where H ? {K1,m1,Pm2}(1?m1?n-k-1,4 ?m2?n-k)];?(Dk,n;H)and ?s(Dk,n;H)of the data center network Dk,n,where H ??K1,m,P4}(1?m?k).