Planar Graph and plane Graph are both topological terms. In graph theory a planar Graph is a collection of objects in space (having x, y, and z coordinates) that are all located on the same plane or slice of space. Specifically a plane would intersect only the nodes of that graph.

Given a planar Graph, if one draws it in a way that no edges cross each other, then it is known as a plane Graph. This is a special case of graphing and not all graphs are plane graphs. A plane Graph is also known as a planar embedding of the graph.
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