A379576 Total numbers of fundamentally distinct graceful labelings of all simple graphs on n vertices.

1, 1, 2, 14, 174, 3655, 122439, 6470268, 526145856, 64906224142

Offset

1,3

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Graceful Labeling.

Example

In the below, G: n stands for "G has n fundamentally distinct graceful labelings".
a(1) = 1 since K_1: 1.
a(2) = 1 since P_2: 1.
a(3) = 2 since P_3: 1, C_3: 1.
a(4) = 14 since C_3+K_1: 1, K_1,3 (claw): 1, diamond: 4, P_4: 1, paw: 5, C_4: 1, K_4: 1

Mathematica

{1, 1} ~ Join ~ Table[Total[GraphData[#, "GracefulLabelingCount"] & /@ GraphData["Graceful", n]], {n, 3, 7}]

Crossrefs

Cf. A333727 (totals of all graceful labelings of simple graphs on n vertices).

Cf. A379575 (totals of all fundamentally distinct graceful labelings of simple graphs on n nodes containing no isolated points).

Sequence in context: A381480 A370909 A377553 * A366736 A300282 A336635

Adjacent sequences: A379573 A379574 A379575 * A379577 A379578 A379579

Keyword

nonn,more,hard

Author

Eric W. Weisstein, Dec 26 2024

Extensions

a(9) from Eric W. Weisstein, Nov 12 2025

a(10) from Eric W. Weisstein, Feb 27 2026

Status

approved