Intrinsic chirality of triple-layered naphthalenophane and related graphs (Q1277804)

As more and more topologically complex molecules are being synthesized, topological techniques become increasingly important in understanding molecular structure. In particular, topology can be a powerful tool in the study of molecular chirality. While chemical chirality is determined on the basis of experimental evidence, we can define a molecular graph to be topologically achiral if it can be deformed to its mirror image, and topologically chiral otherwise. It follows from this definition that if a molecular graph is topologically chiral then the molecule that it represents must be chemically chiral. On the other hand, there exist many chiral molecules whose graphs are topologically achiral, because the deformation which takes the graph to its mirror image cannot be achieved on a chemical level. We prove that the graph of triple-layered naphthalenophane and an infinite class of related graphs are all intrinsically chiral. We also give examples to illustrate that not all graphs which are contractible to a Möbius ladder with three rungs are necessarily intrinsically chiral.