Since all the graphs you are counting are disconnected,
my guess is that there is a combinatorial argument to
determine their number, say L_n, in terms of the number of connected ones.
Assuming you know the number of connected graphs on
k vertices with n edges (where k<=n+1), call it M_{k,n}, my guess
is you should be able to derive a formula for L_n in terms of
the M_{k,n} without needing a computer.
You may need a computer to tabulate the M_{k,n} but maybe
this is done already for "small" n,k?
On Mon, Jan 30, 2023 at 9:38 PM Shiyue Li <shiyue...@brown.edu> wrote:
>
> Hi all,
>
> I am hoping to generate a list of all graph isomorphism classes of a given
> size. The current code that I have first generate all the graphs on 2n, and
> then take all the isomorphism class representatives of size n. But the first
> step of generating all graphs on 2n vertices can take a really long time and
> huge amount of memory (run 10 days on my university's research computing
> cloud) and crashes.
>
> See the following for my code:
>
> def iso_graphs(n):
> '''returns all isomorphism classes of simple graphs on n edges on 2*n
> vertices'''
> L = list(graphs(2 * n, loops=False, size=n)) print("Do we ever reach this
> point?")
> L = [G.canonical_label().copy(immutable=True) for G in L if G.size() == n]
> return L
>
> I wonder if what is a correct and efficient way of doing it.
>
> Thanks!
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-support+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/0acb6537-3fe9-42dc-ab1b-c5c79dd5fb5cn%40googlegroups.com.
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-support+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-support/CAEQuuAX8ApuYCD6Jxp3L3E8YsTNqjd%2BBCZU%3DW-b%3Dx%2BL0110tgA%40mail.gmail.com.
