Hm... technically they're saying that their algorithm performs as well as possible "for every single graph topology". Your special cased algorithm would only wo

Hm... technically they're saying that their algorithm performs as well as possible "for every single graph topology". Your special cased algorithm would only work for one particular graph in a family of isomorphic graphs (unless you have a linear time algorithm for the graph isomorphism problem, in which case please share), but would fail for the rest of the graphs in the family. So I think you could still say that their algorithm performs as well as possible for that topology.