I had this question in my mind for quite sometime:
Given a positive integer $m$, what is the sharpest known bound on the number of non-isomorphic (connected or disconnected) graphs having exactly $m$ edges and no isolated vertex?
I would be happy if there is an upper bound of the form $poly(m)$ or even something like $m^{\log m}$, but I have no idea how to prove or disprove these. Any help will be highly appreciated!