A systematic approach for embedding of Hamiltonian cycles through a prescribed edge in locally twisted cubes

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. The main contribution of this paper is to provide the necessary and sufficient conditions for determining a characterization of permutations of link dimensions constructing Hamiltonian cycles in a locally twisted cube. For those permutations, we propose a linear algorithm for finding a Hamiltonian cycle through a given edge. As a result, we obtain a lower bound for the number of Hamiltonian cycles through a given edge in an n-dimensional locally twisted cube.