# Counting number of simple graphs with 'n' unlabelled vertices.

I am aware that the number of simple graphs possible with $$n$$ labelled vertices is $$2^{n(n-1)/2}$$. Is there any closed formula for the same problem with $$n$$ unlabelled vertices? In case of unlabelled vertices we have to eliminate graphs that are isomorphic.

## 1 Answer

You can find a formula for the counting polynomial using Polya’s Enumeration Theorem as explained in $$(3)$$ of http://mathworld.wolfram.com/SimpleGraph.html