0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 8, 9, 12, 16, 20, 24, 32, 38, 48, 59, 72, 87, 109, 129, 157, 190, 229, 272, 330, 390, 467, 555, 659, 778, 926, 1086, 1283, 1509, 1774, 2074, 2437, 2841, 3322, 3871, 4509, 5236, 6094, 7055, 8181, 9464, 10944, 12624, 14577, 16778, 19322, 22209
Offset: 0
A033483
Number of disconnected 4-valent (or quartic) graphs with n nodes.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 378, 2026, 13351, 104595, 930586, 9124662, 96699987, 1095469608, 13175272208, 167460699184, 2241578965849, 31510542635443, 464047929509794, 7143991172244290, 114749135506381940, 1919658575933845129, 33393712487076999918, 603152722419661386031
Offset: 0
- R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3), this sequence (k=4),
A165655 (k=5),
A165656 (k=6),
A165877 (k=7),
A165878 (k=8),
A185293 (k=9),
A185203 (k=10),
A185213 (k=11).
Disconnected 4-regular simple graphs with girth at least g: this sequence (g=3),
A185244 (g=4),
A185245 (g=5),
A185246 (g=6).
A165626
Number of 5-regular graphs (quintic graphs) on 2n vertices.
Original entry on oeis.org
1, 0, 0, 1, 3, 60, 7849, 3459386, 2585136741, 2807105258926, 4221456120848125, 8516994772686533749, 22470883220896245217626, 75883288448434648617038134, 322040154712674550886226182668
Offset: 0
5-regular simple graphs:
A006821 (connected),
A165655 (disconnected), this sequence (not necessarily connected).
Regular graphs
A005176 (any degree),
A051031 (triangular array), specified degrees:
A000012 (k=0),
A059841 (k=1),
A008483 (k=2),
A005638 (k=3),
A033301 (k=4), this sequence (k=5),
A165627 (k=6),
A165628 (k=7),
A180260 (k=8).
A165653
Number of disconnected 3-regular (cubic) graphs on 2n vertices.
Original entry on oeis.org
0, 0, 0, 0, 1, 2, 9, 31, 147, 809, 5855, 54477, 633057, 8724874, 137047391, 2391169355, 45626910415, 942659626031, 20937539944549, 497209670658529, 12566853576025106, 336749273734805530, 9534909974420181226
Offset: 0
3-regular simple graphs:
A002851 (connected), this sequence (disconnected),
A005638 (not necessarily connected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2), this sequence (k=3),
A033483 (k=4),
A165655 (k=5),
A165656 (k=6),
A165877 (k=7),
A165878 (k=8),
A185293 (k=9),
A185203 (k=10),
A185213 (k=11).
-
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, }][[All, 2]]];
A005638 = A@005638;
A002851 = A@002851;
a[n_] := A005638[[n + 1]] - A002851[[n + 1]];
a /@ Range[0, 20] (* Jean-François Alcover, Jan 21 2020 *)
A165656
Number of disconnected 6-regular (sextic) graphs on n vertices.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 25, 297, 8199, 377004, 22014143, 1493574756, 114880777582, 9919463450855, 955388277929620, 102101882472479938, 12050526046888229845, 1563967741064673811531, 222318116370232302781485, 34486536277291555593662301, 5817920265098158804699762770
Offset: 0
6-regular simple graphs:
A006822 (connected), this sequence (disconnected),
A165627 (not necessarily connected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3),
A033483 (k=4),
A165655 (k=5), this sequence (k=6),
A165877 (k=7),
A165878 (k=8),
A185293 (k=9),
A185203 (k=10),
A185213 (k=11).
A165877
Number of disconnected 7-regular (septic) graphs on 2n vertices.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 1562, 21617036, 733460349818, 42703733735064572, 4073409466378991404239, 613990076321940092226829047, 141518698937232822678583027258225
Offset: 0
7-regular simple graphs:
A014377 (connected), this sequence(disconnected),
A165628 (not necessarily connected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3),
A033483 (k=4),
A165655 (k=5),
A165656 (k=6), this sequence (k=7),
A165878 (k=8),
A185293 (k=9),
A185203 (k=10),
A185213 (k=11).
A165878
Number of disconnected 8-regular simple graphs on n vertices.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 7, 100, 10901, 3470736, 1473822243, 734843169811, 423929978716908, 281768931380519766, 215039290728074333738, 187766225244288486398132, 186874272297562916477691894, 211165081721567703008217979077
Offset: 0
The a(18)=1 graph is K_9+K_9.
8-regular simple graphs:
A014378 (connected), this sequence (disconnected),
A180260 (not necessarily connected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3),
A033483 (k=4),
A165655 (k=5),
A165656 (k=6),
A165877 (k=7), this sequence (k=8),
A185293 (k=9),
A185203 (k=10),
A185213 (k=11).
A185203
Number of disconnected 10-regular graphs with n nodes.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 11, 550, 806174, 2585947720, 9802278927562, 42709859521915286, 214798119408798346811, 1251607430636395979871600, 8463468717232507491862780325, 66406919318277846825588474735084
Offset: 0
10-regular simple graphs:
A014382 (connected), this sequence (disconnected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3),
A033483 (k=4),
A165655 (k=5),
A165656 (k=6),
A165877 (k=7),
A165878 (k=8),
A185293 (k=9), this sequence (k=10),
A185213 (k=11).
A185213
Number of disconnected 11-regular graphs with 2n nodes.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 8037887, 945095928322681, 187549741420313256356540, 66398446859255608487987488813721, 43100445877221052008718432480116589483823
Offset: 0
11-regular simple graphs:
A014384 (connected), this sequence (disconnected).
Disconnected regular simple graphs:
A068932 (any degree),
A068933 (triangular array), specified degree k:
A165652 (k=2),
A165653 (k=3),
A033483 (k=4),
A165655 (k=5),
A165656 (k=6),
A165877 (k=7),
A165878 (k=8),
A185293 (k=9),
A185203 (k=10), this sequence (k=11).
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