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<br> | <br> | ||
| − | <u></u>'''<u>Outline</u>''' | + | <u></u>'''<u>Outline</u>''' |
| − | + | ''<br>'''''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. <br> | 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. <br> | ||
| + | <br> | ||
| + | <u></u>'''Example 1: Square''' | ||
| − | + | '''<br>''' | |
| − | ''' | + | '''Definitions:''' |
| − | + | *'''Burnside''' | |
| − | + | ||
| − | *'''Burnside''' | + | |
*'''Polya''' | *'''Polya''' | ||
| − | '''<br>''' | + | '''<br>''' |
| − | '''Formula:''' | + | '''Formula:''' |
| − | *'''show formula''' | + | *'''show formula''' |
| − | *'''breakdown of each element''' | + | *'''breakdown of each element''' |
*'''relate back to example 1''' | *'''relate back to example 1''' | ||
| − | '''<br>''' | + | '''<br>''' |
| − | '''link to proof''' | + | '''link to proof''' |
| − | '''<br>''' | + | '''<br>''' |
| − | '''References and Additional Information''' | + | '''References and Additional Information''' |
<br> [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | <br> [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | ||
[[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | [[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | ||
Revision as of 11:40, 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
