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A329789 Total number of graceful labelings of connected graphs with n vertices and n edges. 2
0, 0, 2, 12, 68, 400, 2496, 17338, 127660, 1030524, 8852398, 82121018, 806839236, 8481362264, 93933923996, 1104325114202 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

Table of n, a(n) for n=1..16.

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.

Sequence in context: A174327 A245997 A128103 * A245854 A078839 A243771

Adjacent sequences:  A329786 A329787 A329788 * A329790 A329791 A329792

KEYWORD

nonn,more

AUTHOR

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

STATUS

approved

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Last modified June 12 14:45 EDT 2021. Contains 344957 sequences. (Running on oeis4.)