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A335619 Number of fundamentally different graceful labelings of the complete bipartite graph K_{n,n}. 1
1, 1, 4, 1, 7, 2, 10, 3, 8, 1, 42, 2, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
LINKS
Eric Weisstein's World of Mathematics, Complete Bipartite Graph
Eric Weisstein's World of Mathematics, Graceful Labeling
FORMULA
a(n) = A337793(n)/(4*(n!)^2).
EXAMPLE
a(3) = 4 because there are 4 fundamentally different graceful labelings:
solution #1:
0 1 4 5
6 8 14 16
solution #2:
0 1 8 9
10 12 14 16
solution #3:
0 1 2 15
5 9 13 16
solution #4
0 1 2 3:
4 8 12 16
All others can be obtained by permutations of left and right vertices, swapping halves ("0" vertex left or right) and the replacement of all vertex labels k by N^2-k. - noted by Bert Dobbelaere, Oct 01 2020
CROSSREFS
Cf. A337793 (total number of graceful labelings).
Sequence in context: A050356 A245838 A158860 * A037022 A037023 A143971
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Oct 02 2020
EXTENSIONS
a(10)-a(15) from the diagonal of A337278 by Don Knuth, Dec 08 2020
STATUS
approved

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Last modified March 3 16:27 EST 2024. Contains 370512 sequences. (Running on oeis4.)