The generalized 4-connectivity of folded Petersen cube networks

Abstract

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 $ FPQ_{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 $ FPQ_{n, k} $ is $ n+3k-1 $. As a corollary, the generalized 3-connectivity of $ FPQ_{n, k} $ also is obtained and the results on the generalized 4-connectivity of hypercube $ Q_n $ and folded Petersen graph $ FP_k $ can be verified. These conclusions provide a foundation for studying the generalized 4-connectivity of Cartesian product graphs.

Keywords

• generalized 4-connectivity
• folded petersen cube networks
• cartesian product