Complexity of simple undirected graph isomorphism problem
Yes, the best known algorithm is still the algorithm from Babai and Luks, with runtime $\exp(O(\sqrt{n \log n}))$, where $n$ is the number of vertices in the graphs. Unless I'm mistaken, even the best known conondeterministic algorithm for graph isomorphism has exponential runtime. Babai and Luks' algorithm is plausibly near-optimal for deterministic algorithms, but there is much evidence that there is a polynomial time conondeterministic algorithm for graph isomorphism out there to be discovered. In particular, it is known that graph isomorphism is in coAM, and certain circuit lower bounds imply that coAM = coNP.