2007/12/11 by Matt DeVos, DeVos, Matt, Luis Goddyn +5 · 2 citations
Chemistry · Materials Science · Mathematics · #05C10 #05C25 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Graphene research and applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.0712.1631
openalex publication_date 2007/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.