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| − | <u></u><u>Outline</u> | + | <u></u>'''<u>Outline</u>''' |
| − | <br> | + | '''<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> | |
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| + | <u></u>'''Example 1: Square''' | ||
| − | < | + | '''<br>''' |
| − | + | '''Definitions:''' | |
| − | + | *'''Burnside''' | |
| + | *'''Polya''' | ||
| − | + | '''<br>''' | |
| − | + | ||
| − | + | '''Formula:''' | |
| − | + | *'''show formula''' | |
| + | *'''breakdown of each element''' | ||
| + | *'''relate back to example 1''' | ||
| − | + | '''<br>''' | |
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| − | + | '''link to proof''' | |
| − | + | '''<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 11:39, 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
