Topological graph theory

Topological graph theory studies properties of graphs—networks of nodes connected by edges—focusing on how they can be embedded in surfaces without crossing edges. It explores how a graph's structure interacts with the shape of the surface it sits on, such as a plane, sphere, or torus. This field helps understand concepts like planarity (whether a graph can be drawn without crossings), as well as more complex embeddings on different surfaces, revealing deep connections between geometry, topology, and combinatorics. It has applications in circuit design, chemistry, and understanding the fundamental properties of complex networks.