 
Summary: A Picture is Worth
a Thousand Words:
Topological Graph Theory
Dan Archdeacon
Dept. of Math. and Stat.
University of Vermont
Burlington, VT, USA 05405
email: dan.archdeacon@uvm.edu
June 15, 2001
Abstract
Topological graph theory concerns geometric representations of
graphs. In this paper we give a gentle introduction to the area and
survey some of its results and problems.
1 Introduction
A graph is a (nite) set V of vertices together with a set E of edges, where
each edge is an unordered pair of vertices. Graphs are sometimes described by
an adjacency matrix: a jV j jV j symmetric matrix whose rows and columns
are indexed by elements of V , with a 1 in row i column j when fi; jg 2 E
and a 0 otherwise. For example, Figure 1 gives a graph with 10 vertices and
15 edges (each edge gives rise to two 1's in the matrix).
