A351860 Number of minimum cyclic edge cuts in the complete graph K_n.

0, 0, 0, 0, 0, 10, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180, 16215, 17296, 18424, 19600

Offset

1,6

Comments

For n >=6, the cyclic edge connectivity of K_n is 3*(n-3), so a(n) is the number of cyclic edge cuts of that size in K_n.

Links

Table of n, a(n) for n=1..50.

Eric Weisstein's World of Mathematics, Complete Graph

Eric Weisstein's World of Mathematics, Cyclic Edge Connectivity

Eric W. Weisstein, Minimum cyclic edge cuts for K_n

Formula

a(n) = binomial(n,3) = A000292(n-2,3) for n >= 7. - Andrew Howroyd, Jan 28 2023

Mathematica

Table[Piecewise[{{0, n < 6}, {10, n == 6}}, Binomial[n, 3]], {n, 20}] (* Eric W. Weisstein, Nov 23 2024 *)
CoefficientList[Series[x^5 (10 - 5 x - 24 x^2 + 30 x^3 - 10 x^4)/(-1 + x)^4, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 23 2024 *)

Crossrefs

Cf. A000292.

Sequence in context: A022702 A044468 A355491 * A109710 A000447 A052472

Adjacent sequences: A351857 A351858 A351859 * A351861 A351862 A351863

Keyword

nonn,changed

Author

Eric W. Weisstein, Feb 22 2022

Extensions

Terms a(9) and beyond from Andrew Howroyd, Jan 28 2023

Status

approved