Fault-tolerance properties of deBruijn and shuffle-exchange networks

We study node fault-tolerance properties of the d-ary deBruijn and shuffle-exchange networks by appealing to the algebraic structure of their underlying digraphs. In particular, we prove that both of these families of digraphs have connectivity equal to their minimum degree. This result is new in the case of the shuffle-exchange digraphs and can be extended for both families to characterize the pairs of vertices which have a disjoint paths between them. Also, the analysis presented in our results paves the way to a novel deterministic point-to-point routing algorithm which is capable of avoiding a large number of complete shuffle cycles in order-n, d-ary deBruijn and shuffle-exchange digraphs