A simple undirected graph has no self-loops and no parallel edges.
Determine the number of simple undirected graphs $G = (V, E)$ with $V = {1, . . . , n}$
Also, how can I find the number of simple graphs with vertices of degree 1?
Does someone knows a traditional method to solve this? Please help.
Assuming you got $N$ vertices and $M$ edges, then since you got $N$ total vertices, which means that you got $$\sum_{k=1}^{N-1} k = \frac{N(N-1)}{2} = P$$ possible edges. Now out of those $P$, pick the $M$ that are present, i.e. $P \choose M$ :).