  In this paper, following J. Franks' work on Lyapunov graphs of nonsingular
Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on
$S^1 \times S^2$. More precisely, we determine necessary and sufficient
conditions on an abstract Lyapunov graph to be associated with a nonsingular
Smale flow on $S^1 \times S^2$. We also study the singular type vertices in
Lyapunov graphs of nonsingular Smale flows on 3-manifolds.
