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%I #11 Dec 22 2020 12:45:23
%S 1,1,5,26,126,680,3778
%N Maximum number of fundamentally different graceful labelings for a simple graph of n nodes without isolated vertices.
%C 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.)
%D D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a>
%e For n=4 the "paw" graph has a(4)=5 fundamentally different labelings, namely with edges
%e 0-4,0-3,0-2,2-3 or
%e 0-4,0-3,0-2,3-4 or
%e 0-4,0-3,1-3,0-1 or
%e 0-4,0-3,1-3,3-4 or
%e 0-4,0-3,2-4,3-4.
%e The other six graphs with four vertices are either ungraceful (2K_1) or uniquely graceful (K_1,3, K_4, C_4, P_4) or have fewer than 5 (K_1,1,2 has 4).
%e For n=5 the "dart" has a(5)=26 fundamentally different labelings.
%Y Cf. A333728.
%K nonn,more
%O 2,3
%A _Don Knuth_, Dec 21 2020
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