A329788 Total number of graceful labelings of connected graphs with n edges.

1, 2, 6, 24, 116, 672, 4520, 35050, 303468, 2934652, 31145346, 361323708, 4535359000, 61431851046, 890284097146, 13784350300996

Offset: 1

Author

N. J. A. Sloane, Dec 01 2019, based on email from Don Knuth, Dec 01 2019

Keywords

• nonn
• more

Comments

In general, consider a connected graph with E edges and V vertices. The vertices are given labels in the range 0 to E so that the differences between edges' endpoints are {1,...,E}. None of the vertices are isolated; hence each vertex label participates in at least one edge. For this sequence V is unrestricted and E = n.

Links

• D. E. Knuth, Program for counting graceful graph labelings.

Crossrefs

Cf. A033472 (V=E+1), A329789 (V=E). A diagonal of the triangle in A329790.