A333727 Total numbers of graceful labelings of all simple graphs on n nodes.

1, 2, 16, 144, 1428, 25328, 631026, 25087224, 1616380926, 170287969522

Offset

1,2

Comments

Counts are for all labelings, not just fundamental ones, so includes labelings that are equivalent under the graph's automorphism group and via subtractive complementation. - Eric W. Weisstein, Dec 15 2024

Links

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

Eric Weisstein's World of Mathematics, Graceful Labeling.

Eric Weisstein's World of Mathematics, Simple Graph.

Mathematica

{1, 2} ~ Join ~ Table[Total[2 GraphData[#, "AutomorphismCount"] GraphData[#, "GracefulLabelingCount"] & /@ GraphData["Graceful", n]], {n, 3, 7}]

Crossrefs

Cf. A379575 (total numbers of fundamentally distinct graceful labelings among n-node simple graphs having no isolated points).

Cf. A379576 (total numbers of fundamentally distinct graceful labelings among all n-node simple graphs).

Sequence in context: A003768 A214767 A300412 * A024915 A162440 A337793

Adjacent sequences: A333724 A333725 A333726 * A333728 A333729 A333730

Keyword

nonn,more,hard

Author

Eric W. Weisstein, Apr 03 2020

Extensions

a(8) from Eric W. Weisstein, Jul 30 2020

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

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

Status

approved