The generalized 4-connectivity of folded Petersen cube networks

The generalized $\ell$-connectivity ${\kappa }_{\ell }(G)$ of a graph $G$ is a generalization of classical connectivity $\kappa (G)$ with ${\kappa }_2(G)=\kappa (G)$. It serves to measure the capability of connection for any $\ell$ vertices. The folded Petersen cube network $FP{Q}_{n,k}$ can be used to model the topological structure of a communication-efficient multiprocessor. This paper shows that the generalized 4-connectivity of the folded Petersen cube network $FP{Q}_{n,k}$ is $n+3k-1$. As a corollary, the generalized 3-connectivity of $FP{Q}_{n,k}$ also is obtained and the results on the generalized 4-connectivity of hypercube $Q_n$ and folded Petersen graph $F{P}_k$ can be verified. These conclusions provide a foundation for studying the generalized 4-connectivity of Cartesian product graphs.