## Strong Menger connectivity with conditional faults on the class of hypercube-like networks.(English)Zbl 1186.68033

Summary: We study the Menger property on a class of hypercube-like networks. We show that in all $$n$$-dimensional hypercube-like networks with $$n - 2$$ vertices removed, every pair of unremoved vertices $$u$$ and $$v$$ are connected by $$\min \{\deg (u),\deg (v)\}$$ vertex-disjoint paths, where $$\deg (u)$$ and $$\deg (v)$$ are the remaining degree of vertices $$u$$ and $$v$$, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to $$2n - 5$$ vertex faults.

### MSC:

 68M10 Network design and communication in computer systems
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### References:

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