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  • Golden graphs
    Pisanski, Tomaž ; Fowler, Patrick W.
    For a graph with an even number of vertices ▫$n$▫, the HOMO and LUMO eigenvalues ▫$\lambda_H$▫ and ▫$\lambda_L$▫ are respectively equal to the eigenvalues that appear at positions ▫$n/2$▫ and ... ▫$n/2+1$▫ when the spectrum of the adjacency matrix is sorted in non-increasing order. For a graph with an odd number of vertices, ▫$\lambda_H$▫ and ▫$\lambda_L$▫ are both equal to the eigenvalue that appears at position ▫$(n+1)/2$▫ in the order. Using the HOMO-LUMO map as a tool for visualizing the behavior of ▫$\lambda_H$▫ and ▫$\lambda_L$▫ for large sets of chemical and other graphs, it is observed that many graphs have ▫$\lambda_H = \phi^{-1}$▫, where ▫$\phi$▫ is the golden ratio. Some preliminary data on these "golden graphs" are given here for small ▫$n$▫.
    Vir: International journal of chemical modeling. - ISSN 1941-3955 (Vol. 3, iss. 1-2, 2011, str. 7-13)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16560729

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