On Restricted Connectivity and Extra Connectivity of Hypercubes and Folded Hypercubes
Jun‐Ming Xu, Tao Zhou · 上海交通大学学报：英文版 · 2005
Given a graph G and a non-negative integer h, the h-restricted connectivity κ~(h)(G) of G is the minimum cardinality of a set of vertices of G, in which at least h neighbors of any vertex is not included, if any, whose deletion disconnects G and every remaining component has the minimum degree of vertex at least h; and the h-extra connectivity κ_(h)(G) of G is the minimum cardinality of a set of vertices of G, if any, whose deletion disconnects G and every remaining component has order more than h. This paper shows that for the hypercube Q_n and the folded hypercube FQ_n, κ_1(Q_n)=κ~((1))(Q_n)=2n-2 for n≥3, κ_2(Q_n)=3n-5 for n≥4, κ_1(FQ_n)=κ~((1))(FQ_n)=2n for n≥4 and κ~((2))(FQ_n)=4n-4 for n≥8.