Strong Menger Connectivity of Folded Hypercubes with Faulty Subcube

Abstract

Menger-type problems in interconnection networks have received many attentions in recent years. A connected graph [Formula: see text] is strong Menger (edge) connected if there are [Formula: see text] vertex (edge)-disjoint paths joining any two distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. Fault tolerance is an important criterion in the design of interconnection networks. The folded hypercube [Formula: see text] is an important variant of hypercube [Formula: see text] 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 [Formula: see text] [Formula: see text] is strong Menger (edge) connected. Which means that when a subcube [Formula: see text] is faulty, the surviving graph [Formula: see text] is strong Menger (edge) connected. This generalizes the result of [Formula: see text] in [J. Parallel Distrib. Comput. 138 (2020) 190–198].