We present ordered continuations of an abstract Lyapunov semi-graph  and define the Ogasa number for ordered continuations of  New proofs of results on the minimal number of singularities in a Lyapunov graph continuation in [3] and of the handle type decomposition theorem in [1] are provided. Using these results, we obtain lower and upper bounds for the Ogasa number for all possible ordered continuations of

Conley index theory, Morse-Smale flows.