On isomorphisms of finite Cayley graphs—a survey Original Research Article

The isomorphism problem for Cayley graphs has been extensively investigated over the past 30 years. Recently, substantial progress has been made on the study of this problem, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained, and methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the finite simple group classification, through to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.