Graph enumeration

In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph.

The pioneers in this area of mathematics were George Pólya,[2] Arthur Cayley[3] and J. Howard Redfield.

[5] As with combinatorial enumeration more generally, the Pólya enumeration theorem is an important tool for reducing unlabeled problems to labeled ones: each unlabeled class is considered as a symmetry class of labeled objects.

vertices is still not known in a closed-form solution,[6] but as almost all graphs are asymmetric this number is asymptotic to[7]

Various research groups have provided searchable database that lists graphs with certain properties of a small sizes.