Enumeration of Hamiltonian Cycles in $P_4\times P_n$ and $P_5\times P_n$

Abstract

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 $P_5\times P_n$.