planar duality

Planar duality is a relationship between two interconnected graphs drawn on a flat surface without crossing edges. In this relationship, each face (region enclosed by edges) of the original graph corresponds to a vertex in the dual graph, and each edge crossing between faces becomes an edge connecting those vertices in the dual. This creates a mirror-like structure where properties and problems in one graph can be translated into the other, often simplifying analysis. Essentially, planar duality provides a way to study complex connections by transforming the problem into a related, but often easier, dual graph.