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 A385629 #21 Aug 29 2025 19:50:16 %S A385629 0,0,0,0,1,1,2,6,13,56,261 %N A385629 Number of equivalence classes of connected 4-regular graphs on n unlabeled nodes up to local complementation. %C A385629 Number of equivalences classes of 4-regular graphs on n nodes up to a sequence of local complementation or isomorphism. %C A385629 a(n) is necessarily less than: %C A385629 A033301(n) (number of non-isomorphic, not necessarily connected 4-regular graphs); %C A385629 A006820(n) (number of non-isomophic connected 4-regular graphs); %C A385629 A090899(n) (number of local equivalence classes of connected graphs); and %C A385629 A156800(n) (number of equivalence classes for connected graphs up to pivots and isomorphism). %C A385629 This is relevant in the study of optimal quantum circuit synthesis for graph state preparation. %H A385629 Niels Bohr Institute Center for Hybrid Quantum Networks, <a href="https://github.com/nbi-hyq/graph_table">graph_table</a> (github) %H A385629 Tristan Cam, Cyril Gavoille, Yvan Le Borgne, and Simon Martiel, <a href="https://hal.science/hal-05133697/document">Universal Graph Theory Operations for Graph State Preparation</a> %e A385629 There are only two 4-regular graphs with 7 nodes and they are not equivalent up to a sequence of local complementation, thus a(7) = 2. %Y A385629 Cf. A006820, A033301, A090899, A156800. %K A385629 nonn,more,new %O A385629 1,7 %A A385629 _Tristan Cam_, Aug 09 2025