On the extra edge-connectivity of hypercubes

The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G(V,E) is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every remaining component has at least h vertices. This paper shows that the h-extra edge-connectivity of the hypercube Q (n) is a constant 2 (n-1) for < h a parts per thousand currency sign 2 (n-1), and n a parts per thousand yen 4, which extends the result of ["Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161(16): 2753-2757"].