# What is graph canonisation?

In a paper I am working on, I come across a term called "graph canonisation "

According to math-world Wolfram:

A canonical labeling, also called a canonical form, of a graph $G$ is a graph $G^{'}$ which is isomorphic to $G$ and which represents the whole isomorphism class of $G$ (Piperno 2011). The complexity class of canonical labeling is not known

Could one elaborate on that ?

Motivation : I am working on graph isomorphism (See this paper by E.M Luks).

• Very relevant is (Greg Kuperberg's answer in) this thread. Also note the Borel-reducability results of Friedman and Stanley. – Peter Heinig Aug 26 '17 at 10:08