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