 
Summary: Topological Graph Theory
A Survey
Dan Archdeacon
Dept. of Math. and Stat.
University of Vermont
Burlington, VT, USA 05405
email: dan.archdeacon@uvm.edu
1 Introduction
Graphs can be represented in many different ways: by lists of edges, by
incidence relations, by adjacency matrices, and by other similar structures.
These representations are well suited to computer algorithms. Historically,
however, graphs are geometric objects. The vertices are points in space and
the edges are line segments joining select pairs of these points. For example,
the points may be the vertices and edges of a polyhedron. Or they may be the
intersections and traffic routes of a map. More recently, they can represent
computer processors and communication channels. These pictures of graphs
are visually appealing and can convey structural information easily. They
reflect graph theory's childhood in ``the slums of topology.''
Topological graph theory deals with ways to represent the geometric real
ization of graphs. Typically, this involves starting with a graph and depicting
