But already in 1980, another classical theorem—the Babai-Erdős-Selkow theorem—showed that almost all graphs can be relabeled to make easy isomorphism testing possible.

Despite how simple the problem is to state, theoretical computer scientists have struggled for more than 30 years to figure out whether there is any computer algorithm that solves graph isomorphism ...

“Chemists use graph isomorphism testing algorithms to compare molecules and build databases of chemicals,” says Kwan. This allows them to check the novelty of their newly synthesized compounds.