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Solution

A planar graph is a graph that can be drawn on a plane without any two edges crossing each other.

Graph A can be redrawn without edge crossing, so Graph A is planar.

Graph B is similar to $K_{3,3}$ structure. Since $K_{3,3}$ is non-planar, Graph B is not planar.

Graph C also contains a non-planar subdivision structure, so Graph C is not planar.

Therefore, only Graph A is planar.