Planar Graph Definition

Graph Theory · Axiom Academy

LESSON Planar Graph Definition Understanding graphs that can be drawn without edge crossings A graph G = (V, E) is called planar if it can be drawn in the plane such that no two edges intersect except at their endpoints (vertices). Watch as we transform a graph with crossings into a planar embedding: 2. Planar Embedding vs Abstract Graph The abstract graph is defined by its vertices and edges as mathematical objects. A planar embedding is a specific way of drawing that graph in the plane without crossings. Observe how we can create different embeddings of the same graph: 3. Faces (Regions) of a Planar Embedding Once a planar graph is embedded in the plane, it divides the plane into distinct regions called faces . Each face is bounded by edges and vertices. Watch as we identify and color the different faces: Every planar embedding has exactly one unbounded face , also called the outer face or infinite face . This is the region that extends to infinity outside the graph. See how the outer face differs from interior faces: 5. Examples of Planar and Non-Planar Graphs Let's examine concrete examples to solidify our understanding of planarity. Compare planar K₄ with non-planar K₅:

This is the written version of the interactive lesson above. See the full Graph Theory course.