Fault tolerance analysis for hamming graphs with large-scale faulty links based on k-component edge-connectivity

The -ary -dimensional hamming graph is one of the most attractive interconnection networks for parallel processing and computing systems. Analysis of the link fault tolerance of topology structure can provide the theoretical basis for the design and optimization of the interconnection networks. The -component edge-connectivity of an interconnection network , is the minimum number of set of faulty links, such that these malfunctions disconnect the network with at least connected subnetworks. It gives a more precise quantitative analysis of indicators of the robustness of a parallel distributed system in the event of faulty links. Let if is even, and if is odd. In this paper, we prove that the -component edge-connectivity of -ary -dimensional hamming graphs is for , , where represents the maximum degree sum of the subgraph induced by all processors of . As the exact values of -component edge-connectivity of oscillate greatly, an efficient algorithm is designed to determine the exact values of for each and . Our result improves those of Xu et al. and Liu et al. .