planar graph theory

Planar graph theory studies graphs that can be drawn on a flat surface without any edges crossing. These graphs consist of points (vertices) connected by lines (edges), and their key property is whether such a crossing-free drawing exists. Planar graphs are important in fields like computer graphics, network design, and geography, as they help model and analyze systems where overlapping connections are undesirable or impossible. The theory also includes rules, like Euler’s formula, which relates the number of vertices, edges, and faces (regions) created by the drawing, providing insights into the structure and limitations of such graphs.