Recently Lu Sheng-xun has shown how a modified Wang Product can be used to generate all the Hamiltonian cycles in a plane graph with considerably less computation than previously reported. In this paper

Lu’ s algorithm is generalized to nonplanar graphs and named the cycle-algorithm. The dual one called the cut-algorithm is also proposed. It can be used in arbitrary graphs

too. Either of the algorithms is explained in detail by way of an example. Two theorems are derived in which these algorithms have been proved. Both algorithms can be used for finding all of Hamiltonian paths contained in arbitrary graphs. The cut-algorithm has been carried out on the computer Type 719. According to the results from the computer’ s calculation

the number of all Hamiltonian cycles in a certain maximum planar graph with nine vertices should be 112

instead of 96 or 110 given by other authors previously.