Cayley sum graphs and eigenvalues of (3,6)-fullerenes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00206380" target="_blank" >RIV/00216208:11320/09:00206380 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Cayley sum graphs and eigenvalues of (3,6)-fullerenes
Original language 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 {c, -c} 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 {c, -c}. Our proof utilizes a geometric representation to recognize the algebraic structure of these graphs, which turn out to be examples of Cayley sum graphs.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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