Optimal codimension one gradient flows on closed surfaces

We consider codimension one gradient flows on closed surfaces with minimal number of singular points. There are two type of such flow: saddle-node (SN) and saddle connections (SC). We use the chord diagrams to specify flows up to topological trajectory equivivalence. A chord diagram with a marked arc is complete topological invariant of a SN-flow and a chord diagram with T-insert -- of SC-flow. We list all such diagrams for flows on norientable surfaces of genus at most 2 and nonorientable surfaces of genus at most 3. For each of diagram we found inverse one that correspond the inverse flow.