Authors: Olga Bodroža-Pantić ¹; Harris Kwong ²; Milan Pantić ³

• 1 Department of Mathematics and Informatics [Novi Sad]
• 2 Mathematical Sciences Department [Fredonia, NY]
• 3 Department of Physics [Novi Sad]

We study the enumeration of Hamiltonian cycles on the thin grid cylinder graph $C_m \times P_{n+1}$. We distinguish two types of Hamiltonian cycles, and denote their numbers $h_m^A(n)$ and $h_m^B(n)$. For fixed $m$, both of them satisfy linear homogeneous recurrence relations with constant coefficients, and we derive their generating functions and other related results for $m\leq10$. The computational data we gathered suggests that $h^A_m(n)\sim h^B_m(n)$ when $m$ is even.