Enumeration of Hamiltonian Cycles in \(P_4 \times P_n\) and \(P_5 \times P_n\)

A scheme for classifying hamiltonian cycles in \(P_m \times P_n\), is introduced.We then derive recurrence relations, exact and asymptotic values for the number of hamiltonian cycles in \(P_4 \times P_n\) and \(P_5 \times P_n\).