[Nauty-list] Directed graphs with loops

Brendan McKay bdm at cs.anu.edu.au
Sun Sep 12 10:36:49 EST 2010

I believe the number of digraphs with loops is given by OEIS A000595
(this is without any vertex fixed).  Starting at 1 vertex, it is
2, 10, 104, 3044, 291968, 96928992, 112282908928, 458297100061728,
see  http://www.research.att.com/~njas/sequences/A000595 and also
http://www.research.att.com/~njas/sequences/A046858 .

Currently there is no way to make these digraphs directly using the
distributed software. Obviously there should be, and I have added it
to my todo list. Meanwhile there might be some programming hack that
is not too difficult; what size of digraph are you interested in?


* ??????? ?????? <bolgov.ak at gmail.com> [100912 05:08]:
> Hi. Maybe my question is silly, but: I've read the manual and tried to
> generate directed graphs. I used `geng` and `directg` with "-f1". The
> maximum number of directed graphs I could get - 28 (for n=3). But no one of
> them had self-loops. I need all non-isomorphic directed graphs (w/ and w/o
> loops). So, can I generate directed graphs with loops using standart
> resources of gtools? And is there any information about the quantity of
> directed graphs with loops (n=3 for example). Sorry for my bad language.

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