A329789 Total number of graceful labelings of connected graphs with n vertices and n edges.

0, 0, 2, 12, 68, 400, 2496, 17338, 127660, 1030524, 8852398, 82121018, 806839236, 8481362264, 93933923996, 1104325114202

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 E = V = n.

Links

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

Crossrefs

Cf. A033472 (V=E+1), A329788 (any V). A diagonal of the triangle in A329790.