All Bipartite Graphs on n number of vertices I need to find a list of all connected bipartite graphs on 15 vertices. 
http://mapleta.maths.uwa.edu.au/~gordon/remote/graphs/index.html#bips lists all graphs on 14 or fewer number of vertices.
http://oeis.org/A005142 says there are 575 252 112 such graphs.
 A: Try
 geng -bc 15 conbip.g6.txt 
with the program geng from Brendan McKay's nauty package, available from http://cs.anu.edu.au/~bdm/nauty/.
The list of connected bipartite graphs with n = 14 vertices is 74MB compressed and requires a few minutes to generate.  The list for n = 15 may take a while to complete and the resulting file will be large.
A: Simple estimation can be made if one considers selected bipartite graph Gi and then counts all the possible non-bipartite graphs that can be made from this graph Gi by adding inner edges in earch part of the graph Gi. So, if number of vortices in one part is x and number of vertices of another part is n-x, then the total number of new graphs for graph Gi is ((a b) being the binomial coefficient) 2^(x 2)*2(n-x 2)-1. After finding the minimum expression for x, the final estimation is that for each bipartite graph there are additional 2^n^2 non-bipartite graphs. So the part of bipartite graphs goes to zer when n goes to infinity.
From this result it is possible to get estimation of the total number of bipartite graphs on n vertices. 
There are several article that gives exact computation of number of bipartite graphs, but no explicit formulas are given (found).
