Cayley sum graphs and eigenvalues of $(3,6)$-fullerenes
Combinatorics
2007-12-12 v2
Abstract
We determine the spectra of cubic plane graphs whose faces have sizes 3 and 6. Such graphs, "(3,6)-fullerenes", have been studied by chemists who are interested in their energy spectra. In particular we prove a conjecture of Fowler, which asserts that all their eigenvalues come in pairs of the form except for the four eigenvalues . We exhibit other families of graphs which are "spectrally nearly bipartite" in this sense. Our proof utilizes a geometric representation to recognize the algebraic structure of these graphs, which turn out to be examples of Cayley sum graphs.
Cite
@article{arxiv.0712.1631,
title = {Cayley sum graphs and eigenvalues of $(3,6)$-fullerenes},
author = {Matt DeVos and Luis Goddyn and Bojan Mohar and Robert Samal},
journal= {arXiv preprint arXiv:0712.1631},
year = {2007}
}