Planar graphs embed surfaces from "summary" of Introduction to Graph Theory by Douglas Brent West
A planar graph can be drawn in such a way that no edges intersect. This means that the graph can be represented on a flat surface without any edges crossing over each other. However, sometimes a planar graph may not be able to be drawn on a flat surface without edges intersecting. In this case, the graph can still be drawn on a surface with a certain number of holes, known as a surface. The concept of planar graphs embedding surfaces refers to the ability to draw a planar graph on a surface without any edge intersections. This surface can be a sphere, a torus, or any other closed surface. The embedding of a planar graph on a surface is a way of representing the graph without any edge crossings, similar to how it would be represented on a flat surface. When a planar graph is embedded o...
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