Chapter 9 A Graph Theoretic Approach to Atomic Displacements in Fullerenes

Abstract The recently developed idea of analyzing complex networks in terms of node displacement due to vibration (Estrada and Hatano, Chem Phys Lett 486:166–170, 2010a) is applied to fullerenes. The fact that the ramafullerenes (fullerenes of Ramanujan graphs) are limited to fullerenes with relatively small number of C atoms is explained from the point of view of the node displace-ment. The node displacement is also shown to indicate the stability of isomers of C40 fullerenes. It is suggested from the analysis of local node displacement that instability of fullerenes mainly comes from pentagon-rich areas of the molecules. Most of us have been aware of graphite since we were children. We can remem-ber how useful our pencils were in learning to write and the advantage of deleting our errors simply by using rubber erasers. Fewer, however, have had the opportu-nity of admiring the bright and perfection of diamond. For people involved in th