A379395 Maximum number of fundamentally different graceful labelings for a simple graph of n nodes.

1, 1, 1, 5, 26, 126, 680, 3876, 25501, 154231

Offset

1,4

Comments

The difference between "fundamentally different graceful labelings" of a graph and "graceful labelings" of a graph is that the latter is the former multiplied by twice the number of automorphisms. (The extra factor of 2 comes from complementation.)

a(10) >= 154231. - Eric W. Weisstein, Dec 19 2025

Links

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

Eric Weisstein's World of Mathematics, Graceful Labeling.

Eric Weisstein's World of Mathematics, Maximally Graceful Graph.

Eric Weisstein's World of Mathematics, Simple Graph.

Crossrefs

Cf. A339892 (maximum number of fundamentally different graceful labelings excluding graphs with isolated vertices).

Sequence in context: A344218 A247491 A339892 * A244617 A003583 A033115

Adjacent sequences: A379392 A379393 A379394 * A379396 A379397 A379398

Keyword

nonn,more

Author

Eric W. Weisstein, Dec 22 2024

Extensions

a(9) from Eric W. Weisstein, Nov 11 2025

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

Status

approved