Cayley sum graphs and eigenvalues of $(3,6)$-fullerenes
| dc.creator | DeVos, Matt | |
| dc.creator | Goddyn, Luis | |
| dc.creator | Mohar, Bojan | |
| dc.creator | Samal, Robert | |
| dc.date | 2007-12-11 | |
| dc.date | 2007-12-11 | |
| dc.date.accessioned | 2026-07-07T08:48:32Z | |
| dc.date.available | 2026-07-07T08:48:32Z | |
| dc.description | 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 $\{λ,-λ\}$ except for the four eigenvalues $\{3,-1,-1,-1\}$. 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. | |
| dc.identifier | https://arxiv.org/abs/0712.1631 | |
| dc.identifier | http://arxiv.org/abs/0712.1631 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143978 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C50; 05C25; 05C10 | |
| dc.title | Cayley sum graphs and eigenvalues of $(3,6)$-fullerenes | |
| dc.type | text |