[Nauty] counting graphs

[Klas Markström]

On this page http://abel.math.umu.se/~klasm/DATA/ you can find a file 
with the total number of graphs on n vertices for n up to 68 which I 
made a few years ago.
I used a simple Mathematica program to count the graphs in, I 
believe, more or less the same way as Brendan's program did. From the 
timing mentioned my program might a little bit faster, but on the 
other hand it is completely inflexible and can only  compute this one 
thing.
Just thought I'd put the table up in case someone wants the raw 
numbers for something.

/Klas M.

>It isn't GAP, it's Maple.  Converting to C would be a lot
>of work because it relies on the symmetric function package
>SF that you would also need to convert.  If anyone wants
>Maple code for counting graphs I can provide the procedures
>I wrote with Gordon Royle some years ago.  They would also
>be a chore to convert to C as they use series expansions.
>You would also need to use a multiprecision package.
>
>All graphs (not necessarily connected):
>
>                                      1, 1
>                                      2, 2
>                                      3, 4
>                                      4, 11
>                                      5, 34
>                                     6, 156
>                                     7, 1044
>                                    8, 12346
>                                    9, 274668
>                                  10, 12005168
>                                 11, 1018997864
>                                12, 165091172592
>                               13, 50502031367952
>                              14, 29054155657235488
>                            15, 31426485969804308768
>                           16, 64001015704527557894928
>                         17, 245935864153532932683719776
>                       18, 1787577725145611700547878190848
>                     19, 24637809253125004524383007491432768
>                   20, 645490122795799841856164638490742749440
>                21, 32220272899808983433502244253755283616097664
>              22, 3070846483094144300637568517187105410586657814272
>           23, 559946939699792080597976380819462179812276348458981632
>        24, 195704906302078447922174862416726256004122075267063365754368
>     25, 131331393569895519432161548405816890146389214706146483380458576384
>
>Execution time (1GHz Pentium) about 20 seconds.
>
>Brendan.
>
>>  Presumably "GAP" - language. See below.
>>  Someone can use it in GAP or knows how to convert it to C ?
>>
>>  #
>>  # graph - count unlabeled graphs via the Polya-Redfield method.
>>  #
>>  # Calling sequence:
>>  #  graph(n)
>>  #  graph(n,a)
>>...
>
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-- 

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Klas Markström	               email: Klas.Markstrom at math.umu.se
Department of Mathematics        fax:   (+46)90 786 52 22
Umeå University                         phone: (+46)90 786 97 21
S-901 87 Umea, Sweden

URL: http://abel.math.umu.se/~klasm/

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