Toroidal Graphenes from 4-Valent Tori

Square tori are transformed into hexagonal and other tiling tori by several cutting procedures. The toroidal objects thus generated are optimized by a molecular mechanics procedure. The strain energy, defined as the difference between the energy of toroidal structure and the energy of its corresponding straight, open tube, is shown to decrease as the torus diameter increases, in the series 10,n of polyhex tori, up to 5000 atoms. Graph-theoretical characterization of toroidal structures including the Hosoya polynomial, Distance Degree Sequence, and Wiener index is also given.