Let $n \in \mathbb{Z^+}$. Find, with proof, the number of distinct graphs with thevertex set $V = \{1, 2, \ldots,n\}$. We say two such graphs are distinct if one of them has an edge $(u, v)$ and the other one does not have this edge with the same vertices.
Find, with proof, the number of distinct graphs with the vertex set $V = \{1, 2, \ldots,n\}$
graphs;proof techniques;combinatorics