Abstract
Graph Theory 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.
Highlights
A Hamiltonian path of a simple graph is a path that visits each vertex exactly once
A closed Hamiltonian path is called a Hamiltonian cycle or Hamiltonian circuit, which we shall abbreviate as HC
In this paper we investigate, for each fixed m ≥ 2, the generation and enumeration of Hamiltonian cycles on Cm × Pn+1, where n ≥ 1
Summary
We study the enumeration of Hamiltonian cycles on the thin grid cylinder graph Cm × Pn+1. We distinguish two types of Hamiltonian cycles depending on their contractibility (as Jordan curves) and denote their numbers hnmc(n) and hcm(n). For fixed m, both of them satisfy linear homogeneous recurrence relations with constant coefficients. Both of them satisfy linear homogeneous recurrence relations with constant coefficients We derive their generating functions and other related results for m ≤ 10. The computational data we gathered suggests that hnmc(n) ∼ hcm(n) when m is even
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