Fault-Tolerant Cycle Embedding in Balanced Hypercubes with Faulty Vertices and Faulty Edges

Abstract

Let Fv (resp. Fe) be the set of faulty vertices (resp. faulty edges) in the n-dimensional balanced hypercube BHn. The edge-bipancyclicity of BHn − Fv for |Fv| ≤ n − 1 had been proved in [Inform. Sci. 288 (2014) 449–461]. The existence of edge-Hamiltonian cycles in BHn − Fe for |Fe| ≤ 2n − 2 were obtained in [Appl. Math. Comput. 244 (2014) 447–456]. In this paper, we consider fault-tolerant cycle embedding of BHn with both faulty vertices and faulty edges, and prove that there exists a fault-free cycle of length 22n − 2|Fv| in BHn with |Fv| + |Fe| ≤ 2n − 3 and |Fv| ≤ n − 1 for n ≥ 2.