Regular graphs are the graphs in which the degree of each vertex is the same. The [Weisfeiler-Lehman algorithm][1] fails to distinguish between the given two non-isomorphic regular graphs. 

Is there a fastest known algorithm for regular graph isomorphism? Are regular graphs the hardest instance for graph isomorphism? Is there any combinatorial or algebraic technique (group theoretic) to deal with this situation efficiently?

  [1]: https://link.springer.com/chapter/10.1007/978-3-319-57586-5_22