Fault-Tolerant Bipancyclicity of Faulty Hypercubes Under the Generalized Conditional-Fault Model

Let F_v be a set of faulty nodes in an n-dimensional hypercube, denoted by Q_n. Also, let F_e be a set of faulty edges in which at least one end-node of each edge is faulty. An edge in Q_n is said to be critical if it is either fault-free or in F_e. In this paper, we prove that, for up to 2n-4 faulty nodes and/or edges, an n-dimensional hypercube contains a fault-free cycle of every even length from 4 to 2^n-2oF_vo in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature.