The generalized 4-connectivity of folded hypercube
Heqin Liu, Dongqin Cheng · International Journal of Computer Mathematics Computer Systems Theory · 2022
In recent years, a growing number of concepts have been proposed to better assess network fault tolerance, among which the generalized k-connectivity has been widely used in the research of fault tolerance of interconnection networks. For connected graph G, κG(S) refers to the maximum number of internally disjoint trees in G to connect S, where S⊂V(G) with |S|≥2. The generalized k-connectivity of G κk(G)=min{κG(S)∣S⊂V(G),|S|=k}. The n-dimensional folded hypercube FQn, as a hypercube-like network, is obtained by adding 2n−1 edges on n-dimensional hypercube Qn. In this paper, we discuss the generalized 4-connectivity of FQn and show that κ4(FQn)=n for n≥7.