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

Given a graph G and a non-negative integer, the g-extra connectivity (resp. g-extra edge connectivity) of G is the minimum cardinality of a set of vertices (resp. edges) in G, if it exists, whose deletion disconnects G 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 n-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.