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  • Cayley sum graphs and eigenvalues of (3,6)-fullerenes
    DeVos, Matt ...
    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 ▫$\{\lambda, -\lambda\}$▫ except for the four eigenvalues ▫$\{3,-1,-1,-1\}$▫. We exhibit other families of graphs which are "spectrally nearly bipartite" in the sense that nearly all of their eigenvalues come in pairs ▫$\{\lambda, -\lambda\}$▫. Our proof utilizes a geometric representation to recognize the algebraic structure of these graphs, which turn out to be examples of Cayley sum graphs.
    Vir: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 99, no. 2, 2009, str. 358-369)
    Vrsta gradiva - članek, sestavni del
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 15037273

    Povezava(-e):

    http://dx.doi.org/10.1016/j.jctb.2008.08.005

vir: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 99, no. 2, 2009, str. 358-369)

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