[Nauty] counting graphs
Sterten at aol.com
Sterten at aol.com
Fri Dec 13 20:00:01 EST 2002
Klas M. wrote:
>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.
yes, thanks.
Now I know at least that it's possible for ridiculously high n !
Someone on the planet must have it in C ?!?
And maybe for some special graph-classes too...
I take the opportununity to post my X-free graph-counts-table below,
I don't quite understand the patterns/ratios/asymptotics
S-free, S is 4-graph: name , n=1..11 , |Aut|,|,~|
P4-free 1,2,4,10,24, 66, 180, 522, 1532, 4624, 14136, 2,2
pawfree 1,2,4,10,22, 57, 149, 503, 2106, 12668, 106401, 2,2
clawfree 1,2,4,10,26, 85, 302, 1285, 6170, 34294, 227417, 6,2
diamondfree 1,2,4,10,25, 80, 299, 1533, 10886, 114340, 1775162, 4,2
C4-free 1,2,4,10,28,100, 441, 2574, 19849, 201682, 2647684, 8,2
K4-free 1,2,4,10,29,120, 685, 6431,103164, 2894632, 138892304, 24,2
S-free, S is 5-graph: n=1..10 , |Aut|, |{G,G~}| , name
1 2 4 11 33 136 650 3774 24073 169794 2,1 C3=
1 2 4 11 33 132 612 3496 24155 219096 2,2 S3-
1 2 4 11 33 132 607 3524 25350 242893 2,2 C3-,
1 2 4 11 33 132 625 3805 29146 285551 2,2 C4-
1 2 4 11 33 136 685 4550 38123 403093 2,2 P5
1 2 4 11 33 138 713 4981 43232 452330 4,2 S4+e
1 2 4 11 33 136 704 5159 53157 798776 2,2 P4,
1 2 4 11 33 138 746 5898 67605 1127255 4,2 P3,e
1 2 4 11 33 144 835 7392 95965 1786025 8,2 C4,
1 2 4 11 33 138 775 7026 108721 2979011 4,2 P3,,
1 2 4 11 33 140 793 7187 110529 3014419 6,2 S3,
1 2 4 11 33 144 855 8163 125832 3147932 12,2 C3,,
1 2 4 11 33 148 908 8911 137616 3314278 10,1 C5
1 2 4 11 33 144 858 8235 129011 3368681 8,2 e,e,
1 2 4 11 33 144 874 8699 144596 4031510 12,2 C3,e
1 2 4 11 33 144 879 9072 165149 5457803 12,2 e,,,
1 2 4 11 33 146 912 9647 178276 5826451 24,2 S4
1 2 4 11 33 150 986 11416 245440 10164119 120,2 K5
S-free, S is 6-graph: n=1..10 , |Aut|,|,~|
1 2 4 11 34 155 980 9332 120933 1978734 1 ,2
1 2 4 11 34 155 980 9341 122598 2049677 1 ,2
1 2 4 11 34 155 980 9437 127180 2224142 1 ,2
1 2 4 11 34 155 980 9520 134018 2639848 1 ,2
1 2 4 11 34 155 996 10238 161241 3623668 2 ,2
1 2 4 11 34 155 996 10346 168213 4037181 2 ,2
1 2 4 11 34 155 996 10364 171694 4390308 2 ,2
1 2 4 11 34 155 996 10344 170803 4428172 2 ,2
1 2 4 11 34 155 996 10332 170483 4431876 2 ,2
1 2 4 11 34 155 996 10342 170778 4470121 2 ,2
1 2 4 11 34 155 1004 10632 178831 4514529 2 ,2
1 2 4 11 34 155 1004 10646 179633 4522679 2 ,2
1 2 4 11 34 155 1004 10615 178264 4550219 2 ,2
1 2 4 11 34 155 996 10428 176421 4733455 2 ,2
1 2 4 11 34 155 996 10365 174178 4740662 2 ,2
1 2 4 11 34 155 996 10386 175391 4814184 2 ,2
1 2 4 11 34 155 1008 10717 183358 4872229 2 ,2
1 2 4 11 34 155 1004 10673 183080 4897617 2 ,2
1 2 4 11 34 155 996 10439 178530 4970215 2 ,2
1 2 4 11 34 155 1004 10679 184112 4999799 2 ,2
1 2 4 11 34 155 996 10470 181298 5204377 2 ,2
1 2 4 11 34 155 996 10462 181307 5205206 2 ,2
1 2 4 11 34 155 1004 10701 187202 5347078 2 ,2
1 2 4 11 34 155 1008 10802 190083 5395783 2 ,2
1 2 4 11 34 155 1004 10704 187571 5411934 2 ,2
1 2 4 11 34 155 1008 10869 193608 5424082 4 ,2
1 2 4 11 34 155 1014 11072 200805 5735465 4 ,2
1 2 4 11 34 155 1008 10931 198378 5809358 4 ,2
1 2 4 11 34 155 1004 10792 194735 5952163 2 ,2
1 2 4 11 34 155 1008 10933 199260 5954329 4 ,2
1 2 4 11 34 155 1008 10989 202510 6126780 4 ,2
1 2 4 11 34 155 996 10546 190594 6141290 2 ,2
1 2 4 11 34 155 1014 11150 208554 6499253 4 ,2
1 2 4 11 34 155 1008 11009 205977 6571477 4 ,2
1 2 4 11 34 155 1014 11150 209027 6572924 4 ,2
1 2 4 11 34 155 1008 11017 207981 6842668 4 ,2
1 2 4 11 34 155 1008 11057 209755 6891019 4 ,2
1 2 4 11 34 155 1008 11005 207693 6914715 4 ,2
1 2 4 11 34 155 1008 11053 209784 6929241 4 ,2
1 2 4 11 34 155 1020 11355 216710 6932945 4 ,2
1 2 4 11 34 155 1014 11229 214466 6996837 4 ,2
1 2 4 11 34 155 1008 11063 212223 7266262 4 ,2
1 2 4 11 34 155 1008 11118 216093 7576628 4 ,2
1 2 4 11 34 155 1014 11275 220018 7613857 4 ,2
1 2 4 11 34 155 1024 11571 228000 7710779 6 ,2
1 2 4 11 34 155 1012 11285 222628 7844070 6 ,2
1 2 4 11 34 155 1012 11287 223229 7926846 6 ,2
1 2 4 11 34 155 1012 11289 223700 8019184 6 ,2
1 2 4 11 34 155 1020 11515 230010 8090894 8 ,2
1 2 4 11 34 155 1023 11564 231642 8233765 8 ,2
1 2 4 11 34 155 1014 11344 226721 8311558 4 ,2
1 2 4 11 34 155 1017 11444 230021 8335306 8 ,2
1 2 4 11 34 155 1020 11560 233636 8431303 8 ,2
1 2 4 11 34 155 1017 11452 231192 8485718 8 ,2
1 2 4 11 34 155 1023 11611 236071 8696040 8 ,2
1 2 4 11 34 155 1020 11592 237534 8874408 12 ,2
1 2 4 11 34 155 1023 11630 238298 8951263 8 ,2
1 2 4 11 34 155 1020 11596 238697 9074114 12 ,2
1 2 4 11 34 155 1028 11819 244639 9177085 10 ,2
1 2 4 11 34 155 1020 11632 240719 9205057 12 ,2
1 2 4 11 34 155 1020 11628 240786 9255033 12 ,2
1 2 4 11 34 155 1020 11642 242365 9436547 12 ,2
1 2 4 11 34 155 1020 11668 243605 9513142 12 ,2
1 2 4 11 34 155 1031 11913 249754 9587375 12 ,2
1 2 4 11 34 155 1026 11805 248234 9716767 16 ,2
1 2 4 11 34 155 1026 11806 248633 9787527 16 ,2
1 2 4 11 34 155 1020 11719 249898 10285757 12 ,2
1 2 4 11 34 155 1026 11854 253003 10286613 16 ,2
1 2 4 11 34 155 1020 11748 251149 10350526 12 ,2
1 2 4 11 34 155 1024 11870 255878 10636429 24 ,2
1 2 4 11 34 155 1028 11959 258585 10752478 36 ,2
1 2 4 11 34 155 1029 12004 261164 10969624 48 ,2
1 2 4 11 34 155 1029 12005 261394 10997059 48 ,2
1 2 4 11 34 155 1034 12118 264926 11176305 48 ,2
1 2 4 11 34 155 1029 12038 263752 11245842 48 ,2
1 2 4 11 34 155 1034 12132 266257 11343292 72 ,2
1 2 4 11 34 155 1032 12130 267481 11513395 120 ,2
1 2 4 11 34 155 1037 12258 272547 11888559 720 ,2
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