A Graph Theoretic Approach to Atomic Displacements in Fullerenes

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 displacement. 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.