However the complexity-theoretic status of graph isomorphism remains an open question.

That is, it is a graph isomorphism from G to itself.

In practice, graph isomorphism testing is used to avoid some recursive calls.

His paper relates this problem to more abstract graph-theoretical problems, in particular, graph isomorphism.

This result sheds some light on the fact why many reported graph isomorphism algorithms behave well in practice.

Blum and Kannan have shown a program checker for graph isomorphism.

The graph isomorphism problem is low for Parity P ().

He has published many books and papers, primarily on graph isomorphism and chromatic numbers.

In fact, it was later shown that graph isomorphism is low for ZPP.

Graph canonization is the essence of many graph isomorphism algorithms.

These early programs operated mainly on the level of graph isomorphism, checking whether the schematic and layout were indeed identical.

The framework captures problems like factoring, graph isomorphism, and the shortest vector problem.

A number of important special cases of the graph isomorphism problem have efficient, polynomial-time solutions:

This procedure is polynomial-time and gives the correct answer if P is a correct program for graph isomorphism.

One of the more popular classification criteria is graph isomorphism, not to be confused with crystallographic isomorphism.

If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level.

Quadratic non-residuosity and graph isomorphism are also in compIP.

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

The graph isomorphism problem is contained in both NP and co-AM.

(This work also involved deeper math-e-mat-ics related to permutation groups and the graph isomorphism problem.)

There are several competing practical algorithms for graph isomorphism, due to , , , etc.

Also, in organic mathematical chemistry graph isomorphism testing is useful for generation of molecular graphs and for computer synthesis.

Clearly, the graph canonization problem is at least as computationally hard as the graph isomorphism problem.

The Rado graph is, up to graph isomorphism, the only countable graph with the extension property.

If in fact the graph isomorphism problem is solvable in polynomial time, GI would equal P.