Babai's problem


In algebraic graph theory, Babai's problem was 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 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 (Babai Invariant group)

A finite group is called a BI-group if for some inverse closed subsets and of, then for all positive integers.

Open problem

Which finite groups are BI-groups?