The databases contained on this page seek to provide an encompassing list of important properties for exhaustive sets of cubic graphs. The objective is to allow cross-referencing of such properties to identify special cubic graphs of interest to researchers. Each set contains, for all cubic graphs of a given size, a property signature that describes the properties of that graph. The properties currently listed are:
ID number as output by GENREG  with the command: genreg k 3 3
Hamiltonicity (0 for non-Hamiltonian, 1 for Hamiltonian)
Number of undirected Hamiltonian cycles (0 for non-Hamiltonian graphs)
Hyperhamiltonicity (0 for non-Hyperhamiltonian, 1 for Hyperhamiltonian)
Hypohamiltonicity (0 for non-Hypohamiltonian, 1 for Hypohamiltonian)
Planarity (0 for non-planar, 1 for planar)
Bipartiteness (0 for non-bipartite, 1 for bipartite)
Snark (0 for non-Snark, 1 for Snark)
Filar the graph is located in (number of triangles)
Gene (0 for descendant, 1 for gene)
Mutant (0 for non-mutant, 1 for mutant)
Number of ancestor genes (1 if graph is a gene)
Size of largest ancestor gene (the size of the graph for a gene)
Currently the datbases are available for all cubic graphs up to 20 vertices. They can be downloaded individually as text files, or as a combined Excel file.
A 10-vertex graph with the following property signature:
4 1 4 0 0 2 2 3 1 0 0 5 0 0 3 4 2.41421 3
If you believe there are additional properties we should be including in the property signature, please contact Michael Haythorpe.
 M. Meringer: Fast Generation of Regular Graphs and Construction of Cages.Journal of Graph Theory 30, 137-146, 1999.