This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339892 #37 Feb 07 2025 19:35:53 %S A339892 1,1,5,26,126,680,3778 %N A339892 Maximum number of fundamentally different graceful labelings for a simple graph of n nodes without isolated vertices. %C A339892 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.) %C A339892 a(9) >= 22033. - _Eric W. Weisstein_, Feb 07 2025 %D A339892 D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3, in preparation. %H A339892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GracefulLabeling.html">Graceful Labeling</a>. %H A339892 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximallyGracefulGraph.html">Maximally Graceful Graph</a>. %e A339892 For n=4 the "paw" graph has a(4)=5 fundamentally different labelings, namely with edges %e A339892 0-4,0-3,0-2,2-3 or %e A339892 0-4,0-3,0-2,3-4 or %e A339892 0-4,0-3,1-3,0-1 or %e A339892 0-4,0-3,1-3,3-4 or %e A339892 0-4,0-3,2-4,3-4. %e A339892 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 A339892 For n=5 the "dart" has a(5)=26 fundamentally different labelings. %Y A339892 Cf. A333728. %Y A339892 Cf. A379395 (maximum number of fundamentally different graceful labelings allowing graphs with isolated vertices). %K A339892 nonn,more %O A339892 2,3 %A A339892 _Don Knuth_, Dec 21 2020