Topological graph theory
Topological graph theory is the intersection of topology and graph theory, studying graphs embedded in surfaces and other aspects of graphs as topological spaces. Applications of topological graph theory occur in graph drawing, especially the drawing of planar graphs, and computational geometry.
Literature
Standard references on topological graph theory are:
- Gross & Tucker, 1987: Topological graph theory
- Bonnington & Little, 1995: The foundations of topological graph theory (doi)
- Mohar & Thomassen, 2001: Graphs on surfaces (TOC )
Other textbook references include:
- Gross, Yellen, Zhang, edgs., 2013: Handbook of graph theory, 2nd ed. (doi), Ch. 7: Topological graph theory
- Giblin, 2010: Graphs, surfaces, and homology, 3rd ed. (doi), especially Ch. 9: Graphs in surfaces (doi)
- Lando & Zvonkin, 2004: Graphs on surfaces and their applications (doi)
- Book review by Mohar (doi)
- Ellis-Monaghan & Moffatt, 2013: Graphs on surfaces: Dualities, polynomials,
and knots (doi)
- Figure 1.3 helpfully illustrates different representations of graphs on (generally nonorientable) surfaces: cellularly embedded graphs, band decompositions, ribbon graphs, “ram graphs” (ribbon and arrow marked graphs), arrow presentations, and signed rotation systems