On extra connectivity and extra edge-connectivity of balanced hypercubes

摘要

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 byk(g)(G) (resp.lambda(g)( 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.