# Coast to Coast Seminar Series: Live from Burnaby, British Columbia "Spectra of (3,6)-Fullerenes"

*Dr Luis Goddyn*

### Abstract

A (3,6)-Fullerene is a 3-regular planar graph whose faces are triangles and hexagons. Being variants of Buckyballs, these graphs are of interest to chemists. It was conjectured (P.~Fowler, 1995) that the spectrum of any (3,6)-Fullerene consists of opposite real pairs { \pm \lambda }, and four (unpaired) exceptional eigenvalues { 3, -1, -1, -1 }.

We prove this conjecture (and more) by expressing every (3,6)-Fullerene as a Cayley sum graph, a variant of Cayley graph which was introduced by Ben Green in 2003.

This is joint work with Matt DeVos, Robert Samal, and Bojan Mohar.