A graph isomorphism from a simple graph 
to a simple graph 
is a bijection 
such that 
iff 
(West 2000, p. 7). Here 
and 
denote the vertex set and
edge set of 
, respectively, and similarly for 
.
If there is a graph isomorphism for 
to 
, then 
is said to be isomorphic to 
, written 
.
There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. As a result, the special complexity class graph isomorphism complete is sometimes used to refer to the problem of graph isomorphism testing.
