Definitions for "Planar"
A graph is planar if it can be drawn on a plane so that the edges intersect only at the vertices. (For example, of the five first complete graphs all but the fifth, K, is planar.)
Attribute of a graph. A graph is called planar, if it can be drawn in the plane such that there are no edge crossings.
A planar graph is a graph that you can draw on a flat surface, or plane, without any of the edges crossing. Graphs that cannot be drawn on the plane without crossed edges are called non-planar graphs. Any graph that has either of the following graphs as subgraphs are non-planar
adj - Wide in two dimensions, thin in every other dimension. Examples of planar objects are circles, squares, sheets of paper, cd's, the surface of water, etc. See the chart under tetraspace.
involving two dimensions