Linking existing datasets of highly symmetric combinatorial structures and preparing them for use with proof assistants.
Finding links via maniplexes
Our first cross-linked dataset is built around maniplexes — a unifying framework that captures graphs, maps on surfaces, and abstract polytopes in a common language. Maniplexes are matched via canonical forms to existing resources such as the House of Graphs and Potočnik’s censuses of highly symmetric tetravalent graphs.
Download: symob.zip (32,9 MB; Katja Berčič, Gabe Cunningham, Andrés David Santamaría-Galvis, and Janoš Vidali).
Certificates for proof assistants
A collection of certificates witnessing that a graph has the specified group as its full automorphism group. The certificates are given for the 111674 graphs from the combined censuses of connected cubic vertex-transitive graphs on up to 1280 vertices by Potočnik, Spiga and Verret, and of connected cubic symmetric graphs on up to 2048 vertices by Conder.
Automorphism group certificates for cubic vertex-transitive graphs on Zenodo (Janoš Vidali).