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# User:Jason Kimberley/A068934

## A068934

Triangular array C(n,r) that counts the isomorphism classes of connected r-regular simple graphs on n vertices.

For r > 3, these are the output from Markus Meringer's GENREG. The italicised values are from Jason Kimberley running GENREG at The University of Newcastle High Performance Computing Facility for the durations described in the column sequences.

 girth C D E $\ge$ Cge Dge Ege = Ceq Deq Eeq

C D E

Girth at least: 3 4 5 6 7 8

n $\forall$ r 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 A005177 A179184 A002851 A006820 A006821 A006822 A014377 A014378 A014381 A014382 A014384 1 1 1 0 1 1 0 0 1 2 0 0 1 1 2 0 0 1 0 1 5 0 0 1 2 1 1 4 0 0 1 0 2 0 1 17 0 0 1 5 6 3 1 1 22 0 0 1 0 16 0 4 0 1 167 0 0 1 19 59 60 21 5 1 1 539 0 0 1 0 265 0 266 0 6 0 1 18979 0 0 1 85 1544 7848 7849 1547 94 9 1 1 389436 0 0 1 0 10778 0 367860 0 10786 0 10 0 1 50314796 0 0 1 509 88168 3459383 21609300 21609301 3459386 88193 540 13 1 1 2942198440 0 0 1 0 805491 0 1470293675 0 1470293676 0 805579 0 17 0 1 1698517036411 0 0 1 4060 8037418 2585136675 113314233808 733351105934 733351105935 113314233813 2585136741 8037796 4207 21 1 1 0 0 1 0 86221634 0 9799685588936 0 0 9799685588961 0 86223660 0 25 0 1 0 0 1 41301 985870522 2807105250897 2807105258926 985883873 42110 33 1 1 0 0 1 0 11946487647 0 0 0 0 0 11946592242 0 39 0 1 0 0 1 510489 152808063181 152808993767 516344 49 1 1 0 0 1 0 2056692014474 0 0 0 0 0 0 2056701139136 0 60 0 1 0 0 1 7319447 28566273166527 7373924 73 1 1 0 0 1 0 0 0 0 0 0 0 0 0 88 0 1 0 0 1 117940535 118573592 110 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 130 0 1 0 0 1 2094480864 2103205738 158 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 191 0 1 0 0 1 40497138011 40634185402 230 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 273 0 1 0 0 1 845480228069 847871397424 331 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 391 0 1 0 0 1 18941522184590 18987149095005 468 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 0 1 0 0 1 453090162062723 454032821688754 660 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 779 0 1 0 0 1 11523392072541432 11544329612485981 927 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1087 0 1 0 0 1 310467244165539782 310964453836198311 1284 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1510 0 1 0 0 1 8832736318937756165 8845303172513781271 1775 1 1