In 1985, Kroto, Heath, O'Brien, Curl, and Smalley suggested the

structure to explain the pronounced abundance of the

cluster in their graphite laser experiment. A confirmation came in 1990, when a method for bulk production including IR
spectroscopic evidence was delivered by Krätschmer, Lamb, Fostiropoulos, and Huffman. Starting with these two papers, fullerene research exploded.

Theoretical tools are used in modern chemistry to develop molecular models of chemical reactions, processes involving physics and chemistry, events throughout medicine, and toxicology. One aim is to find a quantitative structure-property relationship (QSPR) between the property, e.g. melting point, and the structure of the molecule.

Molar graphs can represent the structural formula of a molecule. Topological indices, polynomials, and spectra of molar graphs are so-called structural invariants.

1. The roots of the Laplacian polynomial of a molecular graph determine the distribution function of the radius of the gyration of a molecule.

2. The min-max values of the spectrum of a molar graph can be used as indicators for graph branching or for the estimation of the HOMO-LUMO separation.

In the Demonstration, one can choose 18 fullerenes from

to

. The molecular graph of the fullerene can be presented as a ball-and-stick figure or a Schlegel diagram. The radio buttons can be used to switch between the results for three structural invariants in a tabular view.

[1] P. W. Fowler and D. E. Manolopoulos,

*An Atlas of Fullerenes*, Oxford: Clarendon Press, 1995.

[2] F. Cataldo, A. Graovac, and O. Ori,

*The Mathematics and Topology of Fullerenes*, New York: Springer, 2011.

[3] M. V. Diudea, I. Gutman, and J. Lorentz,

*Molecular Topology*, Huntington, NY: Nova Science Publishers, 2001.

[4] T. Puzyn, J. Leszczynski, and M. Cronin,

*Recent Advances in QSAR Studies*, New York: Springer, 2010.

[5] J. Gasteiger,

*Handbook of Chemoinformatics*, Weinheim: Wiley-VCH, 2003.