In the following the graphs are assumed to be undirected and simple.
1.Enumerate the number of non-isomorphic graphs on $n$ vetrices where $n$ is fixed.
Here are some ideas I had:
The number of labeled graphs is $ 2^{\frac{n(n-1)}{2}} $.
So it is enough to find the number unlabeled graphs on $n$ vertices.I have no idea for this.
2.Enumerate the number of non-isomorphic graphs on $n$ vertices and $m$ edges where $n,m$ are fixed.
Can we find a closed formula for each of this?
Any help?
Thank you!