Strong Menger Connectivity of Folded Hypercubes with Faulty Subcube

Menger-type problems in interconnection networks have received many attentions in recent years. A connected graph G is strong Menger (edge) connected if there are min{d(G)(u), d(G)(v)} vertex (edge)-disjoint paths joining any two distinct vertices u and v in G. Fault tolerance is an important criterion in the design of interconnection networks. The folded hypercube FQ(n) is an important variant of hypercube Q(n) which remains many desirable properties of hypercube. We consider the strong Menger connectivity of folded hypercubes when part of the network is faulty. We show that FQ(n) - Qs (1 <= s <= n - 1) is strong Menger (edge) connected. Which means that when a subcube Q(s) is faulty, the surviving graph FQ(n) - Q(n) s is strong Menger (edge) connected. This generalizes the result of FQ(n) in [J. Parallel Distrib. Comput. 138 (2020) 190-198].