# Question:How to get all n nodes(n<=15) Non-isomorphic  connected  bipartite graphs?

## Question:How to get all n nodes(n<=15) Non-isomorphic  connected  bipartite graphs?

Maple 2019

I'd like to get all at most 15 vertices Non-isomorphic  connected  bipartite graphs. One way is to use the function NonIsomorphicGraphs(k, output = graphs, outputform = graph, restrictto = connected).

`with(GraphTheory):`

```k:=8; s1:=[NonIsomorphicGraphs(k,restrictto = connected,output=graphs,outputform=graph)]: bipartitegraph:=select[flatten](x->IsBipartite(x)=true, s1): nops(bipartitegraph);```
But when k=9, it is slow, I doubted that the code NonIsomorphicGraphs is not quickly by runing first.

By Checking out the encyclopedia，http://oeis.org/A033995 , we knew the following number of bipartite graphs datas of , at most 14, they are not many（the datas contain  no-connected conditions)

 1, 1, 2, 3, 7, 13, 35, 88, 303, 1119, 5479, 32303, 251135, 2527712

so I read the help document about  NonIsomorphicGraphs.I noticed that one option is :

select=procedure
This allows specification of a procedure to control whether a graph should be included in the output. This provides similar functionality as restrictto but allows for implementation of more complex criteria. Note that this option can be used in combination with restrictto, and only the graphs that satisfy the restrictto criteria will be passed to the select procedure.

But I did not know how to use it.

I 'd like to get a quickly ways to get the bipatite graphs when n is not less than 9.  Any help is awesome.

Ps： I know  in SageMath  we can get all bipartite graphs quikly even though n>=10  by  using the

for g in graphs.nauty_geng('-c -b 10 -g'):

But I hope it can be realized in Maple.

Thanks!

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