Babai's problem
Babai's problem is a problem in algebraic graph theory first proposed in 1979 by László Babai.

Babai's problem 

Let  be a finite group, let  be the set of all irreducible characters of , let  be the Cayley graph (or directed Cayley graph) corresponding to a generating subset   of , and let  be a positive integer.  Is the set 
  
an invariant of the graph ? In other words, does  imply that ?

BI-group 
A finite group  is called a BI-group (Babai Invariant group) if  for some inverse closed subsets  and  of  implies that  for all positive integers .

Open problem 
Which finite groups are BI-groups?

See also
 List of unsolved problems in mathematics
 List of problems solved since 1995

References

Algebraic graph theory
Unsolved problems in graph theory