On 3-Extra Connectivity and 3-Extra Edge Connectivity of Folded Hypercubes
Nai-Wen Chang, Cheng-Yen Tsai, Sun‐Yuan Hsieh · IEEE Transactions on Computers · 2013
Given a graph${\mbi{G}}$and a non-negative integer${{g}}$, the${{g}}$-extra connectivity (resp.${{g}}$-extra edge connectivity) of${\mbi{G}}$is the minimum cardinality of a set of vertices (resp. edges) in${\mbi{G}}$, if it exists, whose deletion disconnects${\mbi{G}}$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${\mbi{n}}$-dimensional folded hypercube is${4}{{n}} - {5}$for${{n}} \geq {6}$(resp.${4}{{n}} - {4}$for${{n}} \geq {5}$). This study also provides an upper bound for the${{g}}$-extra connectivity on folded hypercubes for${{g}} \geq {6}$.