On 3-extra connectivity and 3-extra edge connectivity of folded hypercubes

Given a graph G and a non-negative integer g , 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 4 n-5 for n ≥ 6 (resp. 4 n-4 for n ≥ 5). This study also provides an upper bound for the g-extra connectivity on folded hypercubes for g ≥ 6.