Paths and cycles identifying vertices in twisted cubes

The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The twisted cube is an important variation of the hypercube and preserves many of its desirable properties. Karpovsky et al. introduced the concept of identifying codes to model fault-detection in multiprocessor systems and Honkala et al. developed an identifying code by using cycles to identify the faulty processors in the hypercube. In this paper, we study the vertex identification problem on the twisted cube. We first propose an interesting construction scheme to build paths and cycles, and furthermore apply a minimum number of paths and cycles to identify the faulty processors of the twisted cube.