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We describe all possible topological structures of codimension one gradientvector fields on the shpere with at most ten singular points. To describestructures, we use a graph whose edges are one-dimensional stable manifolds.The saddle-node singularity is specified by selecting a pair of vertices-edgeor edge-face, and the saddle connection is specified by a T-vertex.

Gradient vector fields of codimension one on the 2-sphere with at most ten singular points