A165878 - OEIS

A165878

Number of disconnected 8-regular simple graphs on n vertices.

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

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OFFSET

0,21

LINKS

Table of n, a(n) for n=0..31.

Maciej Demianowicz, Progress in the study of the (non)existence of genuinely unextendible product bases, Quantum Info. Proc. 25 (2026), 67. See also arXiv:2509.26135 [quant-ph], 2025. See references.

Jason Kimberley, Disconnected regular graphs (with girth at least 3)

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Eric Weisstein's World of Mathematics, Disconnected Graph

Eric Weisstein's World of Mathematics, Octic Graph

FORMULA

a(n) = A180260(n) - A014378(n), i.e., Euler_transformation(A014378) - A014378.

a(n) = D(n, 8) in the triangle A068933.

EXAMPLE

The a(18)=1 graph is K_9+K_9.

CROSSREFS

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).

Sequence in context: A357336 A182529 A322909 * A175345 A142358 A210684

Adjacent sequences: A165875 A165876 A165877 * A165879 A165880 A165881

KEYWORD

nonn,hard

AUTHOR

Jason Kimberley, Sep 29 2009

EXTENSIONS

Terms a(26) and beyond from Andrew Howroyd, May 20 2020

STATUS

approved