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Cayley sum graphs and eigenvalues of (3,6)-fullerenesDeVos, 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 delLeto - 2009Jezik - angleškiCOBISS.SI-ID - 15037273
Avtor
DeVos, Matt |
Goddyn, Luis |
Mohar, Bojan |
Šámal, Robert
Teme
matematika |
teorija grafov |
fuleren |
spekter |
geometrična mreža |
mathematics |
grah theory |
(3,6)-cage |
fullerene |
spectrum |
Cayley sum graph |
Cayley additional graph |
geometric lattice |
flat torus
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vir: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 99, no. 2, 2009, str. 358-369)
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DeVos, Matt | ![]() |
Goddyn, Luis | ![]() |
Mohar, Bojan | 01931 |
Šámal, Robert | ![]() |
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