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

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

Offset

1,3

Links

Table of n, a(n) for n=1..8.

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: A167014 A370909 A377553 * A366736 A300282 A336635

Adjacent sequences: A379573 A379574 A379575 * A379577 A379578 A379579

Keyword

nonn,more,new

Author

Eric W. Weisstein, Dec 26 2024

Status

approved