Lyapunov graphs of Non-singular Morse-Smale flows on $S^1 \times S^2$

Following B. Yu's work on Lyapunov graphs of non-singular Smale flows on $S^1\times S^2$, we characterize the Lyapunov graphs of non-singular Morse-Smale flows on $S^1 \times S^2$ by using filtrating neighborhoods as the local data attached to the vertices. More precisely, we determine which oriented graphs with vertices labeled by filtrating neighborhoods can be realized as such Lyapunov graphs.