A394273 Number of ordered graceful labelings of trees with n vertices.

1, 1, 2, 4, 10, 26, 90, 322, 1384, 6576, 34870, 200720, 1272064, 8656004, 63595760

Offset

1,3

Comments

An ordered graceful labeling is a graceful labeling with the additional property that for every vertex, all of its neighbors have labels either all greater than the label of the vertex or all smaller than the label of the vertex.

Links

Table of n, a(n) for n=1..15.

Igor Blokhin, Graph Theory (Python repository)

S. I. El-Zanati, M. J. Kenig, and C. Vanden Eynden, Near alpha-labelings of bipartite graphs, Australasian Journal of Combinatorics, 21 (2000), 275-285.

David A. Sheppard, The factorial representation of balanced labelled graphs, Discrete Math., 15 (1976), no. 4, 379-388.

Crossrefs

Cf. A342225, A033472, A392797.

Sequence in context: A148104 A179981 A086991 * A272603 A272602 A113066

Adjacent sequences: A394270 A394271 A394272 * A394274 A394275 A394276

Keyword

nonn,hard,more

Author

Igor Blokhin, Apr 13 2026

Status

approved