# >> College & Higher Education >> College

How to Use Euler's Theorem to Find the Number of Edges

Leonhard Euler was an 18th-century Swiss mathematician who, among other things, did a certain amount of research in graph theory. He described the relationship between the number of edges, the number of vertices, and the number of faces in a planar graph. There are some constraints associated with this, most notably that edges cannot intersect, but it is a powerful theorem and often used in graph theory.

Instructions

- 1
  Determine the number of faces in the graph. These are the spaces defined by a set of edges. Using a map analogy, if the edges are boundaries between countries, then the faces are the countries. This may be provided to you in the problem, or you may have to determine it from relationships. Note that this includes the infinite, unbounded face, which is the expanse external to all the edges.
- 2
  Determine the number of vertices. In a planar graph, edges are not allowed to intersect, but they are allowed to meet a points called vertices.
- 3
  Add the number of faces and vertices. Then subtract two from this quantity. Supposing that your graph meets all the requisite criteria, most importantly that it is planar, then this is the number of edges.
  
  Euler's formula : vertices ' edges + faces = 2

Pennsylvania Colleges for LD Students

Ranking of California Community Colleges