OFFSET
1,2
COMMENTS
The difference between "fundamentally different graceful labelings" of a graph and "graceful labelings" of a graph is that the latter is the former multiplied by twice the number of automorphisms. (The extra factor of 2 comes from complementation.)
When n>1, the graph K_1,1,n has 2n! automorphisms.
REFERENCES
D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000 (terms 1..48 from Don Knuth)
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Graceful Labeling
MATHEMATICA
A339891[n_]:=If[n==1, 1, DivisorSum[2n+1, 2^((#-1)/2)&]+DivisorSigma[0, n+1]-2^(n-1)-1]; Array[A339891, 50] (* Paolo Xausa, Dec 04 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Don Knuth, Dec 21 2020
STATUS
approved