Want to prove that:
the number of pairwise non-isomorphic connected simple graphs is greater than half of the number of non-isomorphic simple graphs with n vertices.
After observing it is true for small n, my attempt is to prove with induction.
It is obviously true for n=1.
But I am having difficulty in finding the inductive steps. Could someone give some hint?
Update: Since a connected graph with n vertices must have at least n edges, so I consider C(n+1) > g(n)