In this work, In a cubic graph, an edge's number of Hamiltonian cycles is even. This theorem results in an algorithm that provides an exponential lower bound for a given Hamiltonian cycle in such a graph. Complexity of regular graphs or the Hamiltonian cycle in them. Finding the Hamiltonian cycle (or path) of a 3- normal graph was shown to be NP-complete. We show that the task of determining if a k-graph has a Hamiltonian cycle (or path) is NP-complete for every set k≥6 and 3. Determining if a planar k-regular graph has a Hamiltonian cycle (or path) has been shown to be NP-complete for k = 3. We demonstrate that the problem is NP-complete for k = 4 and k = 5