# Ted Dobson: The Cayley Isomorphism Problem

In its most general form, the Cayley Isomorphism Problem asks for necessary and sufficient conditions for two Cayley graphs of a group *G* to be isomorphic. Usually, the "necessary and sufficient conditions" consist of an explicit list of permutations of *G* such that two Cayley graphs of *G* are isomorphic if and only if they are isomorphic by one of the permutations on the list. If this list is *always* as short as possible -- that is, it only consists of automorphisms of *G* -- we say that *G* is a *CI-group with respect to graphs*. Determining whether or not a group is a CI-group with respect to graphs has received considerable attention over the last 40 or so years. In this talk, we will present an overview of this problem, as well as discussing various generalizations of the problem.

Prof. dr. Ted Dobson

Mississippi State University, ZDA