A377502 Number of minimum distinguishing labelings in the cycle graph C_n.

6, 24, 120, 12, 28, 96, 252, 600, 1364, 3048, 6552, 13804, 29040, 59520, 122400, 248472, 504868, 1017840, 2054388, 4126100, 8294444, 16628160, 33349800, 66784536, 133775712, 267736392, 535920696, 1072242540, 2145452092, 4291768320, 8585609340, 17173070880, 34350563940

Offset: 3

Author

Eric W. Weisstein, Oct 30 2024

Keywords

• nonn

Comments

The distinguishing number of the n-cycle graph is 3 for n = 3, 4, 5 and 2 for n >= 6.

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..1000
• Eric Weisstein's World of Mathematics, Cycle Graph.
• Eric Weisstein's World of Mathematics, Distinguishing Number.

Crossrefs

Cf. A032239.

Programs

PARI

a(n)={2*n*if(n<6, if(n>2,[1,3,12][n-2]), sumdiv(n, d, moebius(n/d)*(2^d/n - if(d%2, 2^((d+1)/2), 3*2^(d/2)/2)))/2)} \\ Andrew Howroyd, May 27 2025

Formula

a(n) = 2*n*A032239(n) for n >= 6. - Andrew Howroyd, May 27 2025

Extensions

a(27) onwards from Andrew Howroyd, May 27 2025