Abstract: The present invention is a method of solving the decision, for example, testing if, given a finite number of transformations which can be applied to a finite number of elements, the corresponding n-generated discrete object has a hamiltonian cycle and/or path, searching, for example, obtaining the explicit construction of one several or all the hamiltonian cycles and or paths of the given input, counting, for example, obtaining an upper bound of the number of Hamiltonian cycles and/or paths of the given input and optimization, for example, selecting one of several hamiltonian cycles and/or paths solutions according to an specified criterion, versions of the hamiltonian traversal (cycle and/or path) problem in class of combinatorial discrete objects.