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The fault tolerance of \(k\)-ary \(n\)-cubes with respect to maximally local connectivity. (Chinese. English summary) Zbl 1438.05150

Summary: The \(k\)-ary \(n\)-cube becomes one of the most common interconnection networks for multiprocessor systems because of its good topological property and special structure. The local connectivity of a graph is an important measure for network reliability. Using the local connectivity as the reliability indicator, the maximally local connected graphs are a class of the most reliable networks. It is proved that the \(k\)-ary \(n\)-cube with up to \(2n - 2\) faulty vertices is still maximally local connected.

MSC:

05C40 Connectivity
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