On Graph Isomorphism Complete Problems
Graph Isomorphism Completeness for Perfect Graphs
and Subclasses of Perfect Graphs
C. Boucher D. Loker (2006)



  In this paper, we prove that deciding
  isomorphism of double split graphs, the class of graphs exhibiting a 2-join, and the class of
  graphs exhibiting a balanced skew partition are GI-complete. Further, we show that the GI
  problem for the larger class including these graph classes–that is, the class of perfect graphs–is
  also GI-complete.