# Applications of Burnside's Formula

The applications of Burnside's formula in counting orbits has wide applications (I believe). But, whatever the books I followed on Group Theory, many (or almost all) of the applications mentioned in them are for "coloring problem" which involves roughly coloring vertices of a regular $n$-gon with different colors.

Q. What are the other simple applications of Burnsides theorem which I can present to undergraduates while teaching group theory?

• Counting graphs up to isomorphism (but don't ask me for details). Jan 11, 2015 at 14:32
• Jan 11, 2015 at 14:33
• Here's a list of fifty Burnside lemma and Pólya enumeration theorem examples from this site.
– MJD
Jan 11, 2015 at 14:41
• Thanks very much for useful link @Caranti. Jan 11, 2015 at 15:50
• @Groups, you're welcome! Jan 11, 2015 at 18:19