A systematic approach for embedding distinct Hamiltonian cycles with a prescribed edge in a locally twisted cube

The locally twisted cube interconnection network has been recognized as an attractive alternative to the hypercube network. Previously, the locally twisted cube has been shown to contain a Hamiltonian cycle. In this paper, we propose a systematic approach to develop a linear algorithm for finding a family of Hamiltonian cycles with a given edge in the locally twisted cube. Finally, we obtain a lower bound for the number of Hamiltonian cycles passing through a prescribed edge in an n-dimensional locally twisted cube.