Path embedding in faulty locally twisted cubes

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, fault-tolerant embedding of paths in locally twisted cubes is studied. Let LTQ_n(V,E) denotes the n-dimensional locally twisted cube. We find that, for any faulty set F sub V (LTQ_n)cupE(LTQ_n) with |F| les n - 3 and lscr with 2^n-1 -1 les lscr les |V (LTQ_n -F)| - 1 for any integer n ges 3, a path of length lscr can be embedded between any two distinct nodes with dilation 1 in LTQ_n-F. And, the result does not hold if lscr les 2^n-1-2 or |F| ges n - 2, that is, the two bounds are tight. Moreover, this result extends the known result on (n-3)-Hamiltonian connectivity of LTQ_n in the literature.