The bipanconnectivity of bipartite hypercube-like networks

Abstract Bipanconnectivity is an important parameter in bipartite networks related on the embedding problem of linear arrays and rings. In this paper, we study the fault-tolerant bipanconnectivity of bipartite n-dimensional hypercube-like networks, denoted as B n ′ . We show that for any n-dimensional bipartite hypercube-like network G ∈ B n ′ with f faulty elements (edges and/or vertices), including fv faulty vertices such that f ≤ n − 2 , for each pair of fault-free vertices of distance d in G, there exists a fault-free path of length l linking them, where 2 n − 4 ≤ l ≤ 2 n − 2 f v − 1 and l − d ≡ 0 (mod 2). Our result is optimal when considering the number of faulty elements.