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- W2077169780 abstract "The spectral graph theory is widely used in theoretical chemistry. One of the problems of this theory consists in establishing the relationships between the spectral and structural properties of graphs. The basic spectral characteristics of a graph are its eigenvalues (or coefficients of characteristic polynomial) and eigenvectors, which allow to reconstruct a graph uniquely. The formulae for coefficients of characteristic polynomial of arbitrarily weighted graph in terms of some its subgraphs are well known. This result for a simple graph obtained by H. Sachs in 1964, is called often ‘Sachs' theorem’. The chemical applications of this theorem have been described in the numerous papers. In the present paper, the similar formulae for calculation of eigenvectors of an arbitrarily weighted graph in terms of some its subgraphs are presented and proven. A number of illustrative examples is given and possible chemical applications of this result are briefly discussed." @default.
- W2077169780 created "2016-06-24" @default.
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- W2077169780 date "2005-04-01" @default.
- W2077169780 modified "2023-09-25" @default.
- W2077169780 title "Eigenvectors of weighted graphs: a supplement to Sachs' theorem" @default.
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- W2077169780 doi "https://doi.org/10.1016/j.theochem.2005.01.024" @default.
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