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| − | + | In graph theory, it is sometimes necessary to find the number of ways to color the vertices of a polygon. Two theorems that work together to solve this problem are the Polya theorem and Burnside theorem. | |
Revision as of 11:38, 20 April 2014
We discuss in class colorings of graphs, where adjacent vertices have different colors. Suppose you took the graph to be a polygon and allowed the graph to be reflected and rotated. How many different colorings do you get?
Outline
Introduction
In graph theory, it is sometimes necessary to find the number of ways to color the vertices of a polygon. Two theorems that work together to solve this problem are the Polya theorem and Burnside theorem.
Example 1: Square
Definitions:
- Burnside
- Polya
Formula:
- show formula
- breakdown of each element
- relate back to example 1
link to proof
References and Additional Information
