ATA Lab Seminar "Spectral clustering of combinatorial fullerene isomers based on their facet graph structure"

Speaker: Artur Bille (PhD student at Ulm University, Germany)

After Curl, Kroto and Smalley were awarded 1996 the Nobel Prize in chemistry, fullerenes have been subject of much research. One part of that research is the prediction of a fullerene's stability using topological descriptors. It was mainly done by considering the distribution of the twelve pentagonal facets on its surface. With regard to real-world applications, calculations mostly were performed on all isomers of $C_{40}, C_{60}$ and $C_{80}$. We extend this range, and analyse the spectra of $C_n$ for all feasible $n\leq 150$, and the limit case when $n$ goes to infinity. We suggest a novel method for the classification of combinatorial fullerene isomers using spectral graph theory. The classification presupposes an invariant scheme for the facets based on the Schlegel diagram. The main idea is to find clusters of isomers by constructing a graph invariant using the eigenvalues of matrices representing fullerene graphs. This invariant leads to a linear order within the set of all fullerenes.

ID:  998 175 7123

Please contact organizers (akamyshanova@hse.ru) to recieve the password.