Fault-Tolerant Path-Embedding in Locally Twisted Cubes

Abstract

The locally twisted cube \(LTQ_n\) is an important variation of hypercube and possesses many desirable properties for interconnection networks. In this paper, we investigate the problem of embedding paths in faulty locally twisted cubes. We prove that a path of length \(l\) can be embedded between any two distinct vertices in \(LTQ_n – F\) for any faulty set \(F \subseteq V(LTQ_n) \cup E(LTQ_n)\) with \(|F| \leq n-3\) and any integer \(l\) with \(2^{n-1} \leq l \leq |V(LTQ_n – F)| – 1\) for any integer \(n > 3\). The result is tight with respect to the two bounds on path length \(l\) and faulty set size \(|F|\) for a successful embedding.