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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

Table of n, a(n) for n=2..15.

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

Adjacent sequences:  A335616 A335617 A335618 * A335620 A335621 A335622

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 April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)