Extraconnectivity of hypercubes

Given a graph G and a non-negative integer g, the g-extraconnectivity of G (written κ g ( G ) ) is the minimum cardinality of a set of vertices of G , if it exists, whose deletion disconnects G , and where every remaining component has more than g vertices. The usual connectivity and superconnectivity of G correspond to κ 0 ( G ) and κ 1 ( G ) , respectively. In this work, we determine κ g ( Q n ) for 0 ≤ g ≤ n , n ≥ 4 , where Q n denotes the n -dimensional hypercube.