A308549 Number of connected graceful graphs on n vertices.

1, 1, 2, 6, 18, 106, 819, 10969, 259575, 11686731

Offset

1,3

Links

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

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Graceful Graph

Eric Weisstein's World of Mathematics, Vertex Count

Formula

a(n) = A001349(n) - A308557(n). - Pontus von Brömssen, Dec 29 2024

Example

1 node: K_1
2 nodes: P_2
3 nodes: P_3, C_3
4 nodes: K_1,3 (claw), K_4-e, P_4, paw graph, C_4, K_4
5 nodes: K_2,3, K_1,1,3, K_1,1,1,2, P_5, S_5, W_5 (and 12 more)

Crossrefs

Cf. A001349, A308548 (not necessarily connected), A308557.

Sequence in context: A162064 A162056 A347727 * A212653 A323104 A376932

Adjacent sequences: A308546 A308547 A308548 * A308550 A308551 A308552

Keyword

nonn,more

Author

Eric W. Weisstein, Jun 06 2019

Extensions

a(8) from Eric W. Weisstein, Aug 16 2019

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

a(10) (using formula) from Pontus von Brömssen, Feb 28 2026

Status

approved