On 3-Extra Connectivity and 3-Extra Edge Connectivity of Folded Hypercubes

Given a graph mbiG and a non-negative integer g, the g-extra connectivity (resp. g-extra edge connectivity) of mbiG is the minimum cardinality of a set of vertices (resp. edges) in mbiG, if it exists, whose deletion disconnects mbiG and leaves each remaining component with more than g vertices. This study shows that the 3-extra connectivity (resp. 3-extra edge connectivity) of an mbin-dimensional folded hypercube is 4n - 5 for n ≥ 6 (resp. 4n - 4 for n ≥ 5). This study also provides an upper bound for the g-extra connectivity on folded hypercubes for g ≥ 6.