Total Hamilton Circuits In A Reflected Code Sequence

Abstract:

In certain problems, it is easy to verify a solution if an answer key is available but it may be difficult to generate the answer key in the first place. One such problem lies in addressing the total Hamiltonians on a hypercube Qn. This problem is solved using the direct search method. Using MATLAB, we have generated all possible reflected codes for n-tuples by our customized backtracking method, mirror and rolling method and using a sequential circuit. We also developed a pruning method to obtain the total 430008 Hamiltonians for a 4-cube case. Finally we have compared the performance of our implementations with the existing work to set the future problem statement.

Keywords: Gray Codes, Hamiltonian cycles, algorithm.

Ravindra Singh, Preetam Singh Gour, Preeti Dhatterwal, Sandeep BairwaSuresh Kr. Burdak, Suresh Kr. Borana

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