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 A386962 #15 Aug 29 2025 19:51:26 %S A386962 0,1,2,4,15,60 %N A386962 Number of equivalence classes of connected 3-regular graphs on 2n unlabeled nodes up to local complementation. %C A386962 Number of equivalences classes of 3-regular graphs on 2n nodes up to a sequence of local complementation or isomorphism, also called orbits for the local equivalence relation. %C A386962 a(n) is necessarily less than: %C A386962 A005638(n) (number of non-isomorphic, not necessarily connected 3-regular graphs); %C A386962 A002851(n) (number of non-isomophic connected 3-regular graphs); %C A386962 A090899(n) (number of local equivalence classes of connected graphs); and %C A386962 A156800(n) (number of equivalence classes for connected graphs up to pivots and isomorphism). %C A386962 This is relevant in the study of optimal quantum circuit synthesis for graph state preparation. %H A386962 Niels Bohr Institute Center for Hybrid Quantum Networks, <a href="https://github.com/nbi-hyq/graph_table">graph_table</a> (github) %H A386962 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 A386962 There are only two 3-regular graphs with 6 nodes and they are not equivalent up to a sequence of local complementation, thus a(3) = 2. %Y A386962 Cf. A002851, A005638, A090899, A156800. %K A386962 nonn,more,new %O A386962 1,3 %A A386962 _Tristan Cam_, Aug 11 2025