On extra connectivity and extra edge-connectivity of balanced hypercubes
Huazhong Lü · International Journal of Computer Mathematics · 2016
The balanced hypercube BHn, as a new variation of the hypercube, possesses many attractive properties such that the hypercube dose not have. Given a connected graph G and a non-negative integer g, the g-extra connectivity (resp. g-extra edge-connectivity) of G, denoted by κg(G) (resp. λg(G)), is the minimal cardinality of a set of vertices (resp. edges) of G, if exists, whose deletion disconnects G and each remaining component contains more than g vertices. In this paper, we show that the 2-extra connectivity of BHn is 4n−4 and 2-extra edge-connectivity of BHn is 6n−4 for n≥2. Also, we determine 3-extra connectivity of BHn for n≥2.