Graph enumeration

Summary

Graph enumeration is the part of combinatorics that counts graphs with a given property, either as labelled graphs or up to isomorphism. There are $2^{\binom{n}{2}}$ labelled graphs on $n$ given vertices, and Cayley's formula counts the labelled trees. Unlabelled counts are harder, and tools such as the Pólya enumeration theorem and generating functions are used for them. It is a central part of enumerative combinatorics.